You have a 76.9-mF capacitor initially charged to a potential difference of 10.7

Question

You have a 76.9-mF capacitor initially charged to a potential difference of 10.7 V. You discharge the capacitor through a 4.07-ohm resistor. What is the time constant? After what multiple of the time constant does the potential difference reach 2.17 V?

Time Constant:

Multiple of Time Constant:

You have a 76.9-mF capacitor initially charged to a potential difference of 10.7 V. You discharge the capacitor through a 4.07-0 resistor. What is the time constant? After what multiple of the time constant does the potential difference reach 2.17 V? Time constant: Number Multiple of time constant: Number

Explanation / Answer

RC. Notice that the units of RC is seconds.
RC = 76.9e-3*4.07 = 0.3129s <---------------
Vc(t) = 10.7*e^-t/RC = 2.17
e^-t/0.3129 = 2.17/10.7 = 0.2028
Take natural logs of both sides
-t/0.3129 = Ln(2.17/10.7)
t = -0.3129*Ln(2.17/10.7) = 0.4992s = t when Vc = 2.17V
0.4992/RC = 0.4992/0.3129 = 1.595
So about RC = 0.7962

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