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ECE 222Electric Circuit Analysis II

Chapter 5Duality of

Capacitance & Inductance

Herbert G. Mayer, PSUStatus 2/3/2016

For use at CCUT Spring 2016

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Syllabus Definition Duality Samples Bibliography

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Definition In EE, a dual relationship exists between certain

pairs of electric devices and units, e.g. voltage and current

Duality manifests itself by ability to interchange dual units in an expression, yielding two dual, valid, different expressions

A dual expression is formed by interchanging the two and thus creating a corresponding, dual rule

Ultimate reason behind this is the duality of electrical and magnetic phenomena in nature

Example: v(t) = L di / dt i(t) = H dv / dt

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Duality Samples

Voltage

Capacitance

Resistance

Parallel

Short Circuit

KCL

Impedance

Thévenin TheoremReactance

CurrentInductanceConductanceSerialOpen CircuitKVLAdmittanceNorton TheoremSusceptance

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Duality Samples Resistor & Conductor:

v = i R i = v G

Capacitor & Inductor – differential form:iC = C d vC / dt vL = L d iL / dt

Capacitor & Inductor – integral form:vC(t) = V0 + 1/C iC(t) dt iL(t) = I0 + 1/L vL (t) dt

Voltage Division & Current DivisionvR1 = v * R1 / ( R1 + R2 ) iG1 = i * G1 / ( G1 + G2 )

Inductor Voltage & Capacitor Currentv(t) = L di / dt i(t) = H dv / dt

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Duality Samples

Instantaneous change of current is not possible in an inductorInstantaneous change of voltage at the terminals of an inductor is quite possibleInductor current is out of phase with the voltage by + π/2

Instantaneous change of voltage is not possible in a capacitorInstantaneous change of current (displacement current) in a capacitor is quite possibleCapacitor current (displacement current) is out of phase with the voltage by - π/2

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Bibliography1. Wiki on duality:

https://en.wikipedia.org/wiki/Duality_(electrical_circuits)