Chapter 28, Problem 1ASA

To determine

The $RC$ time constant.

Answer to Problem 1ASA

The $RC$ time constant is the product of the capacitance and the series resistance in a circuit.

Explanation of Solution

Time constant is the product of the capacitance and the series resistance in a circuit. When a capacitor is connected to a battery, its charge build up and the rate of voltage across the capacitor also increases. Similarly, when a charged capacitor is discharged, the rate of voltage decay depends on the same parameters. Both the charging time and discharge time of a capacitor are characterized by time constant.

The expression for time constant is given by,

  $\tau =RC$

Here, $\tau$ is the time constant, $R$ is the resistance, and $C$ is the capacitance.

It is the time required to charge the capacitor, through the resistor, from an initial charge of zero to approximately $63.2\%$ of the value of an applied DC voltage, or to discharge the capacitor through the same resistor to approximately $36.8\%$ of its initial charge voltage.

Conclusion:

Therefore, $RC$ time constant is the product of the capacitance and the series resistance in a circuit.