Using same diagram, Switch S is closed at time t = 0, to begin charging aninitia

Question

Using same diagram, Switch S is closed at time t = 0, to begin charging aninitially uncharged capacitor of capacitance C = 15.0 µF through a resistor of resistance R = 15.0 . At what time is theelectric potential across the capacitor equal is that across theresistor?          t=          ms Using same diagram, Switch S is closed at time t = 0, to begin charging aninitially uncharged capacitor of capacitance C = 15.0 µF through a resistor of resistance R = 15.0 . At what time is theelectric potential across the capacitor equal is that across theresistor?          t=          ms          t=          ms

Explanation / Answer

Let t be the required time Potential difference across C = Potentialdifference across R   V cap =Vres               q / C = i R                   = V C ( 1 - e -t / RC) / C = V / R* e-t /RC * R                 e-t /RC   = ( 1 - e -t / RC)                          e-t/RC   = 1 /2                e t / RC = 2              t = R C ln 2                = 15.0 * 15.0F ln 2                = 0.067 m s

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