A capacitor with an initial potential difference of 126 V is

A capacitor with an initial potential difference of 126 V is discharged through a resistor when a switch between them is closed at t = 0 s. At t = 10.0 s, the potential difference across the capacitor is 1.04 V. (a) What is the time constant of the circuit? (b) What is the potential difference across the capacitor at t = 16.2 s? (?) Number Units (b) Number Units

Solution

a)

potential difference:

    V = V₀e^-t/RC

1.04 = 126 * e^-10/RC

0.008254 = e^-10/RC

ln(0.008254) = -10/RC

ln(0.008254)RC = -10

hence the time constant:

RC =-10/ln(0.008254) = 2.08 s

b)

at t = 16.2 s, the potential difference:

V =126*e^-16.2/2.08

   = 0.053 V