A capacitor with an initial potential difference of 75 V isdischarged through a

Question

A capacitor with an initial potential difference of 75 V isdischarged through a resistor when a switch between them is closedat t = 0. At t = 5.0 s, the potential differenceacross the capacitor is 1.70 V. (a) What is the time constant of thecircuit?
(b) What is the potential difference across the capacitor att = 15.0 s?
A capacitor with an initial potential difference of 75 V isdischarged through a resistor when a switch between them is closedat t = 0. At t = 5.0 s, the potential differenceacross the capacitor is 1.70 V. (a) What is the time constant of thecircuit?
(b) What is the potential difference across the capacitor att = 15.0 s?
(a) What is the time constant of thecircuit?
(b) What is the potential difference across the capacitor att = 15.0 s?

Explanation / Answer

Since V(t)= Vo( e -t ) Vo = 75 and V(5.0) = 1.70 we have V(t) / Vo   = e-t (a) What is the time constant of the circuit? -t = ln(V(t) / Vo   ) plugingin we have - (5.0) = ln(1.70 / 75  ) = - ln(1.70 / 75   ) /5.0= = 0.757 (b) What is the potential difference across the capacitor att = 15.0 s? now since we know V(15.0)= 75( e -0.757 x 15.0 ) V(15.0)= 0.878 mV This is it. Have fun. This is it. Have fun.

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