The capacitors in the figure(Figure 1) are charged and the switch closes at t =0

Question

The capacitors in the figure(Figure 1) are charged and the switch closes at t=0s.

At what time has the current in the 8 ? resistor decayed to half the value it had immediately after the switch was closed?

Express your answer to two significant figures and include the appropriate units.

The capacitors in the figure(Figure 1) are charged and the switch closes at t=0s. At what time has the current in the 8 ? resistor decayed to half the value it had immediately after the switch was closed? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

equivalent resistance

Req =(30*20/30+20)+8

Req =20 ohms

equivalent capacitance

Ceq =(60*60/60+60)+20

Ceq =50 uF

Time constant

T=Req*Ceq =20*50*10^-6

T=1*10^-3 s

given I=Io/2

I=Io e^(-t/T)

Io/2 =Io e^(-t/10^-3)

0.5 =e^(-t/10^-3)

-t/10^-3 =ln(0.5) =-0.693

t =6.93*10^-4 s or 0.693 ms

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