0 ECE 222 Electric Circuit Analysis II Chapter 5 Duality of Capacitance & Inductance Herbert G. Mayer, PSU Status 2/3/2016 For use at CCUT Spring 2016

1 Syllabus Definition Duality Samples Bibliography

2 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

3 Duality Samples Voltage  Capacitance  Resistance  Parallel  Short Circuit  KCL  Impedance  Thévenin Theorem  Reactance  Current Inductance Conductance Serial Open Circuit KVL Admittance Norton Theorem Susceptance

4 Duality Samples Resistor & Conductor: v = i R  i = v G Capacitor & Inductor – differential form: i C = C d v C / dt  v L = L d i L / dt Capacitor & Inductor – integral form: v C (t) = V 0 + 1/C i C (t) dt  i L (t) = I 0 + 1/L v L (t) dt Voltage Division & Current Division v R1 = v * R 1 / ( R 1 + R 2 )  i G1 = i * G 1 / ( G 1 + G 2 ) Inductor Voltage & Capacitor Current v(t)= L di / dt  i(t) = H dv / dt

5 Duality Samples Instantaneous change of current is not possible in an inductor Instantaneous change of voltage at the terminals of an inductor is quite possible Inductor current is out of phase with the voltage by + π/2 Instantaneous change of voltage is not possible in a capacitor Instantaneous change of current (displacement current) in a capacitor is quite possible Capacitor current (displacement current) is out of phase with the voltage by - π/2

6 Bibliography  Wiki on duality: uits)