77-420: Two-terminal components and electrical networks can be connected in series or parallel . The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology . Whether a two-terminal "object" is an electrical component (e.g. a resistor ) or an electrical network (e.g. resistors in series) is a matter of perspective. This article will use "component" to refer to
154-423: A chordal resistance or static resistance , since it corresponds to the inverse slope of a chord between the origin and an I – V curve . In other situations, the derivative d V d I {\textstyle {\frac {\mathrm {d} V}{\mathrm {d} I}}} may be most useful; this is called the differential resistance . In the hydraulic analogy , current flowing through
231-410: A linear approximation is typically used: R ( T ) = R 0 [ 1 + α ( T − T 0 ) ] {\displaystyle R(T)=R_{0}[1+\alpha (T-T_{0})]} where α {\displaystyle \alpha } is called the temperature coefficient of resistance , T 0 {\displaystyle T_{0}}
308-587: A parallel circuit , the voltage is the same for all elements. V = V 1 = V 2 = ⋯ = V n {\displaystyle V=V_{1}=V_{2}=\dots =V_{n}} The current in each individual resistor is found by Ohm's law . Factoring out the voltage gives I = ∑ i = 1 n I i = V ∑ i = 1 n 1 R i . {\displaystyle I=\sum _{i=1}^{n}I_{i}=V\sum _{i=1}^{n}{1 \over R_{i}}.} To find
385-532: A circuit element is characterized not only by the ratio of their magnitudes, but also the difference in their phases . For example, in an ideal resistor , the moment when the voltage reaches its maximum, the current also reaches its maximum (current and voltage are oscillating in phase). But for a capacitor or inductor , the maximum current flow occurs as the voltage passes through zero and vice versa (current and voltage are oscillating 90° out of phase, see image below). Complex numbers are used to keep track of both
462-406: A circuit is called a resistor . Conductors are made of high- conductivity materials such as metals, in particular copper and aluminium. Resistors, on the other hand, are made of a wide variety of materials depending on factors such as the desired resistance, amount of energy that it needs to dissipate, precision, and costs. For many materials, the current I through the material is proportional to
539-835: A coil all turns are in series. Capacitors follow the same law using the reciprocals. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances: [REDACTED] C = ( ∑ i = 1 n 1 C i ) − 1 = ( 1 C 1 + 1 C 2 + 1 C 3 + ⋯ + 1 C n ) − 1 . {\displaystyle C=\left(\sum _{i=1}^{n}{1 \over C_{i}}\right)^{-1}=\left({1 \over C_{1}}+{1 \over C_{2}}+{1 \over C_{3}}+\dots +{1 \over C_{n}}\right)^{-1}.} Equivalently using elastance (the reciprocal of capacitance),
616-892: A complementary relationship: the expression for a series connection of resistances is the same as for parallel connection of conductances, and vice versa. Inductors follow the same law, in that the total inductance of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances: [REDACTED] L = ( ∑ i = 1 n 1 L i ) − 1 = ( 1 L 1 + 1 L 2 + 1 L 3 + ⋯ + 1 L n ) − 1 . {\displaystyle L=\left(\sum _{i=1}^{n}{1 \over L_{i}}\right)^{-1}=\left({1 \over L_{1}}+{1 \over L_{2}}+{1 \over L_{3}}+\dots +{1 \over L_{n}}\right)^{-1}.} If
693-420: A conductor of uniform cross section, therefore, can be computed as R = ρ ℓ A , G = σ A ℓ . {\displaystyle {\begin{aligned}R&=\rho {\frac {\ell }{A}},\\[5pt]G&=\sigma {\frac {A}{\ell }}\,.\end{aligned}}} where ℓ {\displaystyle \ell }
770-542: A resistance of zero. The resistance R of an object is defined as the ratio of voltage V across it to current I through it, while the conductance G is the reciprocal: R = V I , G = I V = 1 R . {\displaystyle R={\frac {V}{I}},\qquad G={\frac {I}{V}}={\frac {1}{R}}.} For a wide variety of materials and conditions, V and I are directly proportional to each other, and therefore R and G are constants (although they will depend on
847-447: A separate loop, the bulbs are said to be in parallel. If the four light bulbs are connected in series, the same current flows through all of them and the voltage drop is 3 volts across each bulb, which may not be sufficient to make them glow. If the light bulbs are connected in parallel, the currents through the light bulbs combine to form the current in the battery, while the voltage drop is 12 volts across each bulb and they all glow. In
SECTION 10
#1733094024738924-418: A series circuit, every device must function for the circuit to be complete. If one bulb burns out in a series circuit, the entire circuit is broken. In parallel circuits, each light bulb has its own circuit, so all but one light could be burned out, and the last one will still function. Series circuits are sometimes referred to as current-coupled. The current in a series circuit goes through every component in
1001-728: A series. Electrical conductance presents a reciprocal quantity to resistance. Total conductance of a series circuits of pure resistances, therefore, can be calculated from the following expression: G = ( ∑ i = 1 n 1 G i ) − 1 = ( 1 G 1 + 1 G 2 + 1 G 3 + ⋯ + 1 G n ) − 1 . {\displaystyle G=\left(\sum _{i=1}^{n}{1 \over G_{i}}\right)^{-1}=\left({1 \over G_{1}}+{1 \over G_{2}}+{1 \over G_{3}}+\dots +{1 \over G_{n}}\right)^{-1}.} For
1078-746: A special case of two conductances in series, the total conductance is equal to: G = G 1 G 2 G 1 + G 2 . {\displaystyle G={\frac {G_{1}G_{2}}{G_{1}+G_{2}}}.} Inductors follow the same law, in that the total inductance of non-coupled inductors in series is equal to the sum of their individual inductances: [REDACTED] L = ∑ i = 1 n L i = L 1 + L 2 + L 3 ⋯ + L n . {\displaystyle L=\sum _{i=1}^{n}L_{i}=L_{1}+L_{2}+L_{3}\cdots +L_{n}.} However, in some situations, it
1155-432: A straight line through the origin with positive slope . Other components and materials used in electronics do not obey Ohm's law; the current is not proportional to the voltage, so the resistance varies with the voltage and current through them. These are called nonlinear or non-ohmic . Examples include diodes and fluorescent lamps . The resistance of a given object depends primarily on two factors: what material it
1232-442: A two-terminal "object" that participates in the series/parallel networks. Components connected in series are connected along a single "electrical path", and each component has the same electric current through it, equal to the current through the network. The voltage across the network is equal to the sum of the voltages across each component. Components connected in parallel are connected along multiple paths, and each component has
1309-457: A voltage drop that interferes with the measurement, so more accurate devices use four-terminal sensing . Many electrical elements, such as diodes and batteries do not satisfy Ohm's law . These are called non-ohmic or non-linear , and their current–voltage curves are not straight lines through the origin. Resistance and conductance can still be defined for non-ohmic elements. However, unlike ohmic resistance, non-linear resistance
1386-415: A wire (or resistor ) is like water flowing through a pipe, and the voltage drop across the wire is like the pressure drop that pushes water through the pipe. Conductance is proportional to how much flow occurs for a given pressure, and resistance is proportional to how much pressure is required to achieve a given flow. The voltage drop (i.e., difference between voltages on one side of the resistor and
1463-587: Is multiple , such as multiple connections for arc lamps . Since electrical conductance G {\displaystyle G} is reciprocal to resistance, the expression for total conductance of a parallel circuit of resistors is simply: G = ∑ i = 1 n G i = G 1 + G 2 + G 3 ⋯ + G n . {\displaystyle G=\sum _{i=1}^{n}G_{i}=G_{1}+G_{2}+G_{3}\cdots +G_{n}.} The relations for total conductance and resistance stand in
1540-465: Is a fixed reference temperature (usually room temperature), and R 0 {\displaystyle R_{0}} is the resistance at temperature T 0 {\displaystyle T_{0}} . The parameter α {\displaystyle \alpha } is an empirical parameter fitted from measurement data. Because the linear approximation is only an approximation, α {\displaystyle \alpha }
1617-454: Is best handled by matrix methods and summing the terms of the inverse of the L {\displaystyle L} matrix (3×3 in this case). The pertinent equations are of the form: v i = ∑ j L i , j d i j d t {\displaystyle v_{i}=\sum _{j}L_{i,j}{\frac {di_{j}}{dt}}} The total capacitance of capacitors in parallel
SECTION 20
#17330940247381694-453: Is different for different reference temperatures. For this reason it is usual to specify the temperature that α {\displaystyle \alpha } was measured at with a suffix, such as α 15 {\displaystyle \alpha _{15}} , and the relationship only holds in a range of temperatures around the reference. The temperature coefficient α {\displaystyle \alpha }
1771-414: Is difficult to prevent adjacent inductors from influencing each other as the magnetic field of one device couples with the windings of its neighbors. This influence is defined by the mutual inductance M. For example, if two inductors are in series, there are two possible equivalent inductances depending on how the magnetic fields of both inductors influence each other. When there are more than two inductors,
1848-408: Is equal to the sum of their individual capacitances: Terminal (electronics) A terminal is the point at which a conductor from a component , device or network comes to an end. Terminal may also refer to an electrical connector at this endpoint, acting as the reusable interface to a conductor and creating a point where external circuits can be connected. A terminal may simply be
1925-440: Is equal to the sum of their individual resistances: [REDACTED] R = ∑ i = 1 n R i = R 1 + R 2 + R 3 ⋯ + R n . {\displaystyle R=\sum _{i=1}^{n}R_{i}=R_{1}+R_{2}+R_{3}\cdots +R_{n}.} Here, the subscript s in R s denotes "series", and R s denotes resistance in
2002-414: Is exactly -90° or +90°, respectively, and X and B are nonzero. Ideal resistors have an angle of 0°, since X is zero (and hence B also), and Z and Y reduce to R and G respectively. In general, AC systems are designed to keep the phase angle close to 0° as much as possible, since it reduces the reactive power , which does no useful work at a load. In a simple case with an inductive load (causing
2079-452: Is higher than expected. Similarly, if two conductors near each other carry AC current, their resistances increase due to the proximity effect . At commercial power frequency , these effects are significant for large conductors carrying large currents, such as busbars in an electrical substation , or large power cables carrying more than a few hundred amperes. The resistivity of different materials varies by an enormous amount: For example,
2156-406: Is known as a parallel circuit . Many circuits can be analyzed as a combination of series and parallel circuits, along with other configurations . In a series circuit, the current that flows through each of the components is the same, and the voltage across the circuit is the sum of the individual voltage drops across each component. In a parallel circuit, the voltage across each of the components
2233-411: Is made of metal, usually platinum, while a thermistor is made of ceramic or polymer.) Resistance thermometers and thermistors are generally used in two ways. First, they can be used as thermometers : by measuring the resistance, the temperature of the environment can be inferred. Second, they can be used in conjunction with Joule heating (also called self-heating): if a large current is running through
2310-435: Is made of, and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area; for example, a thick copper wire has lower resistance than an otherwise-identical thin copper wire. Also, for a given material, the resistance is proportional to the length; for example, a long copper wire has higher resistance than an otherwise-identical short copper wire. The resistance R and conductance G of
2387-459: Is not always true in practical situations. However, this formula still provides a good approximation for long thin conductors such as wires. Another situation for which this formula is not exact is with alternating current (AC), because the skin effect inhibits current flow near the center of the conductor. For this reason, the geometrical cross-section is different from the effective cross-section in which current actually flows, so resistance
Series and parallel circuits - Misplaced Pages Continue
2464-506: Is not constant but varies with the voltage or current through the device; i.e., its operating point . There are two types of resistance: Also called chordal or DC resistance This corresponds to the usual definition of resistance; the voltage divided by the current R s t a t i c = V I . {\displaystyle R_{\mathrm {static} }={V \over I}.} Also called dynamic , incremental , or small-signal resistance It
2541-399: Is often undesired, particularly in the case of transmission losses in power lines . High voltage transmission helps reduce the losses by reducing the current for a given power. On the other hand, Joule heating is sometimes useful, for example in electric stoves and other electric heaters (also called resistive heaters ). As another example, incandescent lamps rely on Joule heating:
2618-438: Is only true in the special cases of either DC or reactance-free current. The complex angle θ = arg ( Z ) = − arg ( Y ) {\displaystyle \ \theta =\arg(Z)=-\arg(Y)\ } is the phase difference between the voltage and current passing through a component with impedance Z . For capacitors and inductors , this angle
2695-433: Is quantified by resistivity or conductivity . The nature of a material is not the only factor in resistance and conductance, however; it also depends on the size and shape of an object because these properties are extensive rather than intensive . For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. All objects resist electrical current, except for superconductors , which have
2772-417: Is related to their microscopic structure and electron configuration , and is quantified by a property called resistivity . In addition to geometry and material, there are various other factors that influence resistance and conductance, such as temperature; see below . Substances in which electricity can flow are called conductors . A piece of conducting material of a particular resistance meant for use in
2849-1012: Is resistance, G is conductance, X is reactance , and B is susceptance . These lead to the complex number identities R = G G 2 + B 2 , X = − B G 2 + B 2 , G = R R 2 + X 2 , B = − X R 2 + X 2 , {\displaystyle {\begin{aligned}R&={\frac {G}{\ G^{2}+B^{2}\ }}\ ,\qquad &X={\frac {-B~}{\ G^{2}+B^{2}\ }}\ ,\\G&={\frac {R}{\ R^{2}+X^{2}\ }}\ ,\qquad &B={\frac {-X~}{\ R^{2}+X^{2}\ }}\ ,\end{aligned}}} which are true in all cases, whereas R = 1 / G {\displaystyle \ R=1/G\ }
2926-422: Is shining on them. Therefore, they are called photoresistors (or light dependent resistors ). These are a common type of light detector . Superconductors are materials that have exactly zero resistance and infinite conductance, because they can have V = 0 and I ≠ 0 . This also means there is no joule heating , or in other words no dissipation of electrical energy. Therefore, if superconductive wire
3003-548: Is that the resistivity itself may depend on frequency (see Drude model , deep-level traps , resonant frequency , Kramers–Kronig relations , etc.) Resistors (and other elements with resistance) oppose the flow of electric current; therefore, electrical energy is required to push current through the resistance. This electrical energy is dissipated, heating the resistor in the process. This is called Joule heating (after James Prescott Joule ), also called ohmic heating or resistive heating . The dissipation of electrical energy
3080-459: Is the ohm ( Ω ), while electrical conductance is measured in siemens (S) (formerly called the 'mho' and then represented by ℧ ). The resistance of an object depends in large part on the material it is made of. Objects made of electrical insulators like rubber tend to have very high resistance and low conductance, while objects made of electrical conductors like metals tend to have very low resistance and high conductance. This relationship
3157-406: Is the derivative of the voltage with respect to the current; the slope of the current–voltage curve at a point R d i f f = d V d I . {\displaystyle R_{\mathrm {diff} }={{\mathrm {d} V} \over {\mathrm {d} I}}.} When an alternating current flows through a circuit, the relation between current and voltage across
Series and parallel circuits - Misplaced Pages Continue
3234-462: Is the length of the conductor, measured in metres (m), A is the cross-sectional area of the conductor measured in square metres (m ), σ ( sigma ) is the electrical conductivity measured in siemens per meter (S·m ), and ρ ( rho ) is the electrical resistivity (also called specific electrical resistance ) of the material, measured in ohm-metres (Ω·m). The resistivity and conductivity are proportionality constants, and therefore depend only on
3311-413: Is the same, and the total current is the sum of the currents flowing through each component. Consider a very simple circuit consisting of four light bulbs and a 12-volt automotive battery . If a wire joins the battery to one bulb, to the next bulb, to the next bulb, to the next bulb, then back to the battery in one continuous loop, the bulbs are said to be in series. If each bulb is wired to the battery in
3388-409: Is typically +3 × 10 K−1 to +6 × 10 K−1 for metals near room temperature. It is usually negative for semiconductors and insulators, with highly variable magnitude. Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon strain . By placing a conductor under tension (a form of stress that leads to strain in the form of stretching of
3465-600: The current in a component with resistance R i {\displaystyle R_{i}} , use Ohm's law again: I i = V R i . {\displaystyle I_{i}={\frac {V}{R_{i}}}\,.} The components divide the current according to their reciprocal resistances, so, in the case of two resistors, I 1 I 2 = R 2 R 1 . {\displaystyle {\frac {I_{1}}{I_{2}}}={\frac {R_{2}}{R_{1}}}.} An old term for devices connected in parallel
3542-471: The 24-volt system. If two or more components are connected in parallel, they have the same difference of potential (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applied to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff's current law . In
3619-444: The article: Electrical resistivity and conductivity . For the case of electrolyte solutions, see the article: Conductivity (electrolytic) . Resistivity varies with temperature. In semiconductors, resistivity also changes when exposed to light. See below . An instrument for measuring resistance is called an ohmmeter . Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes
3696-437: The circuit, and are denoted by solid circles. All electrochemical cells have two terminals ( electrodes ) which are referred to as the anode and cathode or positive (+) and negative (-). On many dry batteries , the positive terminal (cathode) is a protruding metal cap and the negative terminal (anode) is a flat metal disc (see Battery terminal ) . In a galvanic cell such as a common AA battery , electrons flow from
3773-436: The circuit. Therefore, all of the components in a series connection carry the same current. A series circuit has only one path through which its current can flow. Opening or breaking a series circuit at any point causes the entire circuit to "open" or stop operating. For example, if even one of the light bulbs in an older-style string of Christmas tree lights burns out or is removed, the entire string becomes inoperable until
3850-600: The coils are tightly coupled there can be near short circuit conditions and high circulating currents for both positive and negative values of M , which can cause problems. More than three inductors become more complex and the mutual inductance of each inductor on each other inductor and their influence on each other must be considered. For three coils, there are three mutual inductances M 12 {\displaystyle M_{12}} , M 13 {\displaystyle M_{13}} and M 23 {\displaystyle M_{23}} . This
3927-468: The conductivity of teflon is about 10 times lower than the conductivity of copper. Loosely speaking, this is because metals have large numbers of "delocalized" electrons that are not stuck in any one place, so they are free to move across large distances. In an insulator, such as Teflon, each electron is tightly bound to a single molecule so a great force is required to pull it away. Semiconductors lie between these two extremes. More details can be found in
SECTION 50
#17330940247384004-589: The conductor), the length of the section of conductor under tension increases and its cross-sectional area decreases. Both these effects contribute to increasing the resistance of the strained section of conductor. Under compression (strain in the opposite direction), the resistance of the strained section of conductor decreases. See the discussion on strain gauges for details about devices constructed to take advantage of this effect. Some resistors, particularly those made from semiconductors , exhibit photoconductivity , meaning that their resistance changes when light
4081-483: The end of a wire or it may be fitted with a connector or fastener . In network analysis , terminal means a point at which connections can be made to a network in theory and does not necessarily refer to any physical object. In this context, especially in older documents, it is sometimes called a pole . On circuit diagrams, terminals for external connections are denoted by empty circles. They are distinguished from nodes or junctions which are entirely internal to
4158-674: The faulty bulb is replaced. I = I 1 = I 2 = ⋯ = I n {\displaystyle I=I_{1}=I_{2}=\cdots =I_{n}} In a series circuit, the current is the same for all of the elements. In a series circuit, the voltage is the sum of the voltage drops of the individual components (resistance units). V = ∑ i = 1 n V i = I ∑ i = 1 n R i {\displaystyle V=\sum _{i=1}^{n}V_{i}=I\sum _{i=1}^{n}R_{i}} The total resistance of two or more resistors connected in series
4235-401: The filament is heated to such a high temperature that it glows "white hot" with thermal radiation (also called incandescence ). The formula for Joule heating is: P = I 2 R {\displaystyle P=I^{2}R} where P is the power (energy per unit time) converted from electrical energy to thermal energy, R is the resistance, and I is the current through
4312-712: The inductors are situated in each other's magnetic fields, this approach is invalid due to mutual inductance. If the mutual inductance between two coils in parallel is M , the equivalent inductor is: L = L 1 L 2 − M 2 L 1 + L 2 − 2 M {\displaystyle L={\frac {L_{1}L_{2}-M^{2}}{L_{1}+L_{2}-2M}}} If L 1 = L 2 {\displaystyle L_{1}=L_{2}} L = L + M 2 {\displaystyle L={\frac {L+M}{2}}} The sign of M {\displaystyle M} depends on how
4389-423: The last two groups can be combined. The first three terms represent the sum of the self-inductances of the various coils. The formula is easily extended to any number of series coils with mutual coupling. The method can be used to find the self-inductance of large coils of wire of any cross-sectional shape by computing the sum of the mutual inductance of each turn of wire in the coil with every other turn since in such
4466-413: The magnetic fields influence each other. For two equal tightly coupled coils the total inductance is close to that of every single coil. If the polarity of one coil is reversed so that M is negative, then the parallel inductance is nearly zero or the combination is almost non-inductive. It is assumed in the "tightly coupled" case M is very nearly equal to L . However, if the inductances are not equal and
4543-399: The material the wire is made of, not the geometry of the wire. Resistivity and conductivity are reciprocals : ρ = 1 / σ {\displaystyle \rho =1/\sigma } . Resistivity is a measure of the material's ability to oppose electric current. This formula is not exact, as it assumes the current density is totally uniform in the conductor, which
4620-830: The mutual inductance between each of them and the way the coils influence each other complicates the calculation. For a larger number of coils the total combined inductance is given by the sum of all mutual inductances between the various coils including the mutual inductance of each given coil with itself, which is termed self-inductance or simply inductance. For three coils, there are six mutual inductances M 12 {\displaystyle M_{12}} , M 13 {\displaystyle M_{13}} , M 23 {\displaystyle M_{23}} and M 21 {\displaystyle M_{21}} , M 31 {\displaystyle M_{31}} and M 32 {\displaystyle M_{32}} . There are also
4697-482: The negative terminal to the positive terminal, while the conventional current is opposite to this. Electrical conductance The electrical resistance of an object is a measure of its opposition to the flow of electric current . Its reciprocal quantity is electrical conductance , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical friction . The SI unit of electrical resistance
SECTION 60
#17330940247384774-409: The other), not the voltage itself, provides the driving force pushing current through a resistor. In hydraulics, it is similar: the pressure difference between two sides of a pipe, not the pressure itself, determines the flow through it. For example, there may be a large water pressure above the pipe, which tries to push water down through the pipe. But there may be an equally large water pressure below
4851-1245: The phase and magnitude of current and voltage: u ( t ) = R e ( U 0 ⋅ e j ω t ) i ( t ) = R e ( I 0 ⋅ e j ( ω t + φ ) ) Z = U I Y = 1 Z = I U {\displaystyle {\begin{array}{cl}u(t)&=\operatorname {\mathcal {R_{e}}} \left(U_{0}\cdot e^{j\omega t}\right)\\i(t)&=\operatorname {\mathcal {R_{e}}} \left(I_{0}\cdot e^{j(\omega t+\varphi )}\right)\\Z&={\frac {U}{\ I\ }}\\Y&={\frac {\ 1\ }{Z}}={\frac {\ I\ }{U}}\end{array}}} where: The impedance and admittance may be expressed as complex numbers that can be broken into real and imaginary parts: Z = R + j X Y = G + j B . {\displaystyle {\begin{aligned}Z&=R+jX\\Y&=G+jB~.\end{aligned}}} where R
4928-491: The phase to increase), a capacitor may be added for compensation at one frequency, since the capacitor's phase shift is negative, bringing the total impedance phase closer to 0° again. Y is the reciprocal of Z ( Z = 1 / Y {\displaystyle \ Z=1/Y\ } ) for all circuits, just as R = 1 / G {\displaystyle R=1/G} for DC circuits containing only resistors, or AC circuits for which either
5005-409: The pipe, which tries to push water back up through the pipe. If these pressures are equal, no water flows. (In the image at right, the water pressure below the pipe is zero.) The resistance and conductance of a wire, resistor, or other element is mostly determined by two properties: Geometry is important because it is more difficult to push water through a long, narrow pipe than a wide, short pipe. In
5082-404: The reactance or susceptance happens to be zero ( X or B = 0 , respectively) (if one is zero, then for realistic systems both must be zero). A key feature of AC circuits is that the resistance and conductance can be frequency-dependent, a phenomenon known as the universal dielectric response . One reason, mentioned above is the skin effect (and the related proximity effect ). Another reason
5159-411: The resistance of wires, resistors, and other components often change with temperature. This effect may be undesired, causing an electronic circuit to malfunction at extreme temperatures. In some cases, however, the effect is put to good use. When temperature-dependent resistance of a component is used purposefully, the component is called a resistance thermometer or thermistor . (A resistance thermometer
5236-435: The resistor, the resistor's temperature rises and therefore its resistance changes. Therefore, these components can be used in a circuit-protection role similar to fuses , or for feedback in circuits, or for many other purposes. In general, self-heating can turn a resistor into a nonlinear and hysteretic circuit element. For more details see Thermistor#Self-heating effects . If the temperature T does not vary too much,
5313-409: The resistor. Near room temperature, the resistivity of metals typically increases as temperature is increased, while the resistivity of semiconductors typically decreases as temperature is increased. The resistivity of insulators and electrolytes may increase or decrease depending on the system. For the detailed behavior and explanation, see Electrical resistivity and conductivity . As a consequence,
5390-407: The same voltage across it, equal to the voltage across the network. The current through the network is equal to the sum of the currents through each component. The two preceding statements are equivalent, except for exchanging the role of voltage and current . A circuit composed solely of components connected in series is known as a series circuit ; likewise, one connected completely in parallel
5467-555: The same way, a long, thin copper wire has higher resistance (lower conductance) than a short, thick copper wire. Materials are important as well. A pipe filled with hair restricts the flow of water more than a clean pipe of the same shape and size. Similarly, electrons can flow freely and easily through a copper wire, but cannot flow as easily through a steel wire of the same shape and size, and they essentially cannot flow at all through an insulator like rubber , regardless of its shape. The difference between copper, steel, and rubber
5544-409: The size and shape of the object, the material it is made of, and other factors like temperature or strain ). This proportionality is called Ohm's law , and materials that satisfy it are called ohmic materials. In other cases, such as a transformer , diode or battery , V and I are not directly proportional. The ratio V / I is sometimes still useful, and is referred to as
5621-842: The three self-inductances of the three coils: M 11 {\displaystyle M_{11}} , M 22 {\displaystyle M_{22}} and M 33 {\displaystyle M_{33}} . Therefore L = ( M 11 + M 22 + M 33 ) + ( M 12 + M 13 + M 23 ) + ( M 21 + M 31 + M 32 ) {\displaystyle L=\left(M_{11}+M_{22}+M_{33}\right)+\left(M_{12}+M_{13}+M_{23}\right)+\left(M_{21}+M_{31}+M_{32}\right)} By reciprocity, M i j {\displaystyle M_{ij}} = M j i {\displaystyle M_{ji}} so that
5698-840: The total resistance of all components, add the reciprocals of the resistances R i {\displaystyle R_{i}} of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance: [REDACTED] R = ( ∑ i = 1 n 1 R i ) − 1 = ( 1 R 1 + 1 R 2 + 1 R 3 + ⋯ + 1 R n ) − 1 {\displaystyle R=\left(\sum _{i=1}^{n}{1 \over R_{i}}\right)^{-1}=\left({1 \over R_{1}}+{1 \over R_{2}}+{1 \over R_{3}}+\dots +{1 \over R_{n}}\right)^{-1}} For only two resistances,
5775-527: The total series elastance equals the sum of each capacitor's elastance. Two or more switches in series form a logical AND ; the circuit only carries current if all switches are closed. See AND gate . A battery is a collection of electrochemical cells . If the cells are connected in series, the voltage of the battery will be the sum of the cell voltages. For example, a 12 volt car battery contains six 2-volt cells connected in series. Some vehicles, such as trucks, have two 12 volt batteries in series to feed
5852-616: The unreciprocated expression is reasonably simple: R = R 1 R 2 R 1 + R 2 . {\displaystyle R={\frac {R_{1}R_{2}}{R_{1}+R_{2}}}.} This sometimes goes by the mnemonic product over sum . For N equal resistances in parallel, the reciprocal sum expression simplifies to: 1 R = N 1 R . {\displaystyle {\frac {1}{R}}=N{\frac {1}{R}}.} and therefore to: R = R N . {\displaystyle R={\frac {R}{N}}.} To find
5929-481: The voltage V applied across it: I ∝ V {\displaystyle I\propto V} over a wide range of voltages and currents. Therefore, the resistance and conductance of objects or electronic components made of these materials is constant. This relationship is called Ohm's law , and materials which obey it are called ohmic materials. Examples of ohmic components are wires and resistors . The current–voltage graph of an ohmic device consists of
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