The charge on a C = 0.4F capacitor is measured as a function of time in a physics lab and producesfollowing graph. The capacitor is part of a simple circuit having only a battery, a capacitor, and a resistor inseries. The capacitor starts uncharged and at t=0s, the battery is plugged in and the capacitor charges. Ingeneral, the charge of a charging capacitor is given by:q(t) = Qmax(1 – e-t/RC)Charge vs. Time20181614O 12106.42378.10Time (s)Chart AreaUse the graph to estimate the time constant for this circuit, r.Estimate the resistance of the resistor R in this circuit.Charge (C)00

Answered: The charge on a C = 0.4F capacitor is…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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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

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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