Physics

Capacitors Solutions

+ Charging and Discharging a Capacitor in an R-C Circuit
q(t) =
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Learning Goal:
To understand the dynamics of a series R-C circuit.
Consider a series circuit containing a resistor of resistance R and a
capacitor of capacitance C connected to a source of EMF E with
negligible internal resistance. The wires are also assumed to have
zero resistance. Initially, the switch is open and the capacitor
discharged. (Figure 1)
Part 1
Now differentiate q (t) to obtain an expression for the current I(t).
Express your answer in terms of any or all of E, R, t, and C. Enter exp(x) for et
Let us try to understand the processes that take place after the switch
is closed. The charge of the capacitor, the current in the circuit, and,
correspondingly, the voltages across the resistor and the capacitor, will
be changing. Note that at any moment in time during the life of our
circuit, Kirchhoffs loop rule holds and indeed, it is helpful:
E - VR - Vc =0, where Vr is the voltage across the resistor, and
Vc is the voltage across the capacitor.
IVO AO
?
I(t) =
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Part J
Figure
1 of 2
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Find the time to that it would take the charge of the capacitor to reach 99.99% of its maxir
Express your answer numerically in seconds. Use three significant figures in your
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R
W
IVO AEO
?
10=0
to =
C
%=0
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Let us now consider a different R-C circuit This time, the capacitor is initially charged (q(0) - 90