Posted by Lanise on Wednesday, February 10, 2010 at 11:02pm.
A capacitor in a singleloop RC circuit is charged to 64% of its final voltage in 1.5 s.
Find the time constant for the circuit.
Find the percentage of the circuit's final voltage after 3.9 s .
Vc/Vi= %

College physics  drwls, Thursday, February 11, 2010 at 1:01am
The voltage across the capacitor is
Vi * [1  e^(t/RC)]
in this type of circuit. Vi is the power supply voltage. RC is the time constant.
The final voltage is Vi.
When t = RC (the time constant), the voltage is
Vc = Vi*[1  e^1] = 0.632 Vi
When t = 1.5 s,
0.64 Vi = Vs * [1  e^(t/RC)]
e^(t/RC)= 0.36
t/RC = 1.02
RC = 1.5/1.02 = 1.47 seconds
That is the time constant.
After 3.9 s
Vc = Vi* [1  e^(3.9/1.47)]
= 0.930 Vi
Unless you show some work on future posts here, I will not be assisting you again. Perhaps someone else will.
Vc = Vi* [1  e^(3.9/1.47)]
= 0.930 Vi
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