# Equivalent circuit

Discussion in 'General Electronics Chat' started by chua, Jul 14, 2010.

1. ### chua Thread Starter New Member

Mar 21, 2010
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Consider a capacitor connected in series with a 5ohm resistor and a zener diode of 20v. The voltage across the 5ohm resistor at time t will be 10e^(-t/5C) and so the current will be 2e^(-t/5C). Since resistance is define as ration between voltage and current the resistance seen by the zener diode by the capacitor at time t will be 10e^(t/5C). So can we say that the resistance seen by the capacitor at time t will be 5+10e^(t/5C)? It is obvious to see that V(t) for the capacitor is 20+10e^(-t/5C). By using I=-Cdv/dt, i try whether i can obtain the same v(t) by using the equation V/5+10e^(t/5C)=-Cdv/dt and i integrate the equation by using integration by substitution method and get back the same answer for v(t) which is 20+10e^(-t/5C).

By using voltage divider formula also, the voltage drop across zener diode
v(t)*R(t)/5+R(t)=20+10e^(-t/5C)*10e^(t/5C)/(10e^(t/5C)+5)=20

At here, can we say that in a circuit diagram which consist a capacitor connected in series with a resistor and a zener diode have the same electrical properties as the circuit diagram which consist of a capacitor connected in series with the same resistor and 20v voltage supply or a "virtual resistor" which has the same parameter as R(t)? Such concept is also applicable to other electrical component right?such as an active regulator?