(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the circuit below, where C_{1}=80mF, C_{2}=30mF, R=50ohms and E=5V.

At t=0, both capacitors are uncharged - so it's charging.

The circuit is in series, with E ---> C_{1}---> C_{2}---> R ---> (back to) E

a) Find the time constant.

b) The initial potential difference across R.

c) The current at t=3s.

d) The potential difference across C2, at t=3s.

2. Relevant equations

C=Q/V

V=IR

X=X_{max}(e^(-t/RC)) (where X is I, V or Q and is decreasing with time)

X=X_{max}(1 -e^{(-t/RC)}) (where X is I, V or Q and is increasing with time)

3. The attempt at a solution

Here are my answers, can someone check if I'm right?

a)

time constant = RC = (50 ohms)(21.8 mF) = 1.09 s

b)

V=5.0 ohms (same as E)

c)

V=RI -> 5V=(50 ohms)I -> I=0.1 A

I=I_{max}(e^{-t/RC})

I=(0.1 A)[/SUB](e^{(-3s/1.09s)})

I=6.37x10^{-3}A

d)

V_{Ceq}= V_{max}(1-e^{-t/RC})

V_{Ceq}= (5 V)(1-e^{-3s/1.09s})

V_{Ceq}= 4.68 V

V=C/Q -> 4.68V=30mF/Q -> Q=6.4x10^{-3}C

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# Homework Help: RC Circuit, Charging, Question

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