Question

Switch S in in the figure is closed at time t = 0, to begin charging an initially uncharged capacitor of capacitance C = 17.1 ?F through a resistor of resistance R = 20.4 ?. At what time is the potential across the capacitor equal to that across the resistor?

Answer 1

For a series RC circuit, the expression for the voltage across the capacitor is -

V= Eo e ^ -t/RC

[Where V is the emf across the capacitor and Eo is the original emf supplied]

Now at some instant the V= Eo / 2 because both the resistor and the capacitor have the same emf so V+V = Eo

therefore -
1/2 = e^(-t/rc)

=> ln(1/2) = -t/RC

=> t = - RC * ln(1/2) ( which is the same as RC * ln(2) )

put the values -

t = 17.1 *10^-6 *20.4 * ln(2)

=0.000242 sec

Therefore the requisite time is 0.000242 sec.