**Problem 3:**A 10 mF capacitor is charged in series with a 50Ω resistor using a 1.5V battery.a) What is the time constant of the circuit?b) If you wanted the capacitor to charge more slowly, what resistor should you substitute, a 10Ω one or a 100Ω one? Explain.

Answered: a) What is the time constant of the…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter10: Direct-current Circuits

Section: Chapter Questions

Problem 96CP: Consider the circuit below. The capacitor has a capacitance of 10 mF. The switch is closed and after...

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**Problem 3:**

A 10 mF capacitor is charged in series with a 50Ω resistor using a 1.5V battery.

a) What is the time constant of the circuit?

b) If you wanted the capacitor to charge more slowly, what resistor should you substitute, a 10Ω one or a 100Ω one? Explain.

Expert Solution

Step 1: Know the basic concepts for a RC circuit:

For a series RC circuit, the charge on a charging capacitor at any time $t$ is given as,

$Q left parenthesis t right parenthesis equals C V subscript 0 left square bracket 1 minus e to the power of negative t over tau end exponent right square bracket$ (1)

where $Q left parenthesis t right parenthesis$ is the charge on the capacitor at any time $t$ , $V subscript 0$ is the initial potential difference across the capacitor, $C$ is the capacitance, and $tau$ is the time constant.

The time constant for a series RC circuit is given by the formula.

$tau equals R C$ (2)

where $tau$ is the time constant, $R$ is the resistance, and $C$ is the capacitance of the circuit.

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