Chapter 19, Problem 87GP

To determine

The value of the resistance $R$ .

Answer to Problem 87GP

The value of the resistance $R$ is $7.23\Omega$ .

Explanation of Solution

Given information:

The power rating of the bulb is $2.5\text{W}$ and voltage is $3\text{V}$ . The bulb is connected to a battery of $9\text{V}$ .

Consider the given circuit.

Formula used:

Write the expression to calculate the current flowing through the bulb using Ohm’s law.

  $P=VI$    … (1)

Apply Kirchhoff’s voltage law in the circuit.

  $-V_b+RI+V=0$    … (2)

Calculation:

Substitute the values in equation (1).

  $\begin{array}{c}2.5=3\times I\\ I=0.83\text{A}\end{array}$

Substitute the values in equation (2).

  $\begin{array}{c}-9+R\times 0.83+3=0\\ 0.83R=9-3\\ R=\frac{6}{0.83}\\ =7.23\Omega \end{array}$

Therefore, the value of the resistance $R$ is $7.23\Omega$ .