The charge on a C = 0.4F capacitor is measured as a function of time in a physics lab and produces following graph. The capacitor is part of a simple circuit having only a battery, a capacitor, and a resistor in series. The capacitor starts uncharged and at t=0s, the battery is plugged in and the capacitor charges. In general, the charge of a charging capacitor is given by: q(t) = Qmax(1 – e-t/RC) Charge vs. Time 20 18 16 14 O 12 10 6. 4 2 3 7 8. 10 Time (s) Chart Area Use the graph to estimate the time constant for this circuit, r. Estimate the resistance of the resistor R in this circuit. Charge (C) 00

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Chapter19: Capacitors
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The charge on a C = 0.4F capacitor is measured as a function of time in a physics lab and produces
following graph. The capacitor is part of a simple circuit having only a battery, a capacitor, and a resistor in
series. The capacitor starts uncharged and at t=0s, the battery is plugged in and the capacitor charges. In
general, the charge of a charging capacitor is given by:
q(t) = Qmax(1 – e-t/RC)
Charge vs. Time
20
18
16
14
O 12
10
6.
4
2
3
7
8.
10
Time (s)
Chart Area
Use the graph to estimate the time constant for this circuit, r.
Estimate the resistance of the resistor R in this circuit.
Charge (C)
00
Transcribed Image Text:The charge on a C = 0.4F capacitor is measured as a function of time in a physics lab and produces following graph. The capacitor is part of a simple circuit having only a battery, a capacitor, and a resistor in series. The capacitor starts uncharged and at t=0s, the battery is plugged in and the capacitor charges. In general, the charge of a charging capacitor is given by: q(t) = Qmax(1 – e-t/RC) Charge vs. Time 20 18 16 14 O 12 10 6. 4 2 3 7 8. 10 Time (s) Chart Area Use the graph to estimate the time constant for this circuit, r. Estimate the resistance of the resistor R in this circuit. Charge (C) 00
Expert Solution
Step 1

Whenever an input is applied to the RC network, the capacitor will take some time to reach its final value. The time constant is the time required by the network to reach 63.2% of final value.

Step 2

a). Time constant:

From the graph, the 63.2% of final charge value is

=0.632*20=12.64

The time required to reach the charge value of 12.64 is 2.4seconds.

So, the time constant=2.4s

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