Chapter 19, Problem 7Q

To determine

Change in power supply, when two identical resistances are connected in series instead of one.

Answer to Problem 7Q

Solution:

The battery needs to supply only half the power.:

Explanation of Solution

Given:

Two identical resistor of resistance, $R$

Battery

Formula used:

The power of the light bulb is given as

        $P=\frac{V^2}{R}$

Here,

        $P$ is the power

        $V$ is the voltage

        $R$ is the resistance of the bulb

Calculation:

The initial power supplied by the battery when there is only one resistance is connected

        $P=\frac{V^2}{R}$…… (1)

The total resistance of the circuit when two resistors connected in series connection

        $\begin{array}{c}{R}_T=R+R\\ =2R\end{array}$

The power supplied by the battery when two resistors are connected in series is calculated as

        $P=\frac{V^2}{2R}$…… (2)

It’s clear from the Eq. (1)and Eq. (2), that only half the power is required when two resistors are connected in series connection.