Growth of current in a C-R circuit
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Three capacitors each with capacitance C and a parallel combination of two resistances R each are connected in series with an ideal battery of emf V as in figure.
a) What is the time constant of the circuit?
b) If the switch is closed at time t = 0; find an expression for the current in the circuit as a function of time.
c) What is the charge that accumulates on the left plate of the first capacitor, after a long time when the switch is closed?
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Solution Summary
A complex circuit with capacitors and resistors is connected to a battery. The switch is closed at t=0 The growth of current and other quantities are calculated.
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Question: Three capacitors each with capacitance C and a parallel combination of two resistances R each are connected in series with an ideal battery of emf V as in figure.
a) What is the time constant of the circuit?
b) If the switch is closed at time t = 0; find an expression for the current in the circuit as a function of time.
c) What is the charge that accumulates on the left plate of the first capacitor, after a long time when the switch is closed?
a) The time constant of R-C circuit is given by
τ= CR
The equivalent capacitance of the three capacitors in series is given by
1/C_eq = 1/C+1/C+1/C=3/C ...
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