A capacitor with an initial potential difference of 100V is discharged through a

Question

A capacitor with an initial potential difference of 100V is discharged through a resistor when a switch between them is closed at t=0. At t=10 second the potential difference across the capacitor is 1.00 V. A) what is the time constant of the circuit? B) what is the potential difference across the capacitor at t=17.0 second? A capacitor with an initial potential difference of 100V is discharged through a resistor when a switch between them is closed at t=0. At t=10 second the potential difference across the capacitor is 1.00 V. A) what is the time constant of the circuit? B) what is the potential difference across the capacitor at t=17.0 second? A) what is the time constant of the circuit? B) what is the potential difference across the capacitor at t=17.0 second?

Explanation / Answer

Given,

potential difference of 100V

switch between them is closed at t=0

potential difference across the capacitor is 1.00 V.

t=10 second

a)

the time constant of the circuit is

V(t)=V0e-t/RC

1=100e-10/RC

0.01=e-10/RC

ln(0.01)=-10/RC

ln(0.01)RC=-10

RC=-10/ln(0.01)

=2.17

b)

the potential difference across the capacitor at t=17.0 second is

V(17)=100e-17/2.17

V(17)=0.0396V

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