Chapter 22, Problem 87A

To determine

Higher resistance bulb.

Answer to Problem 87A

50 W bulb has higher resistance.

Explanation of Solution

Given:

Circuit voltage, $V=120\text{V}$

Power rating of first lightbulb, $P_1=50\text{W}$

Power rating of second lightbulb, $P_2=100\text{W}$

Formula Used:

The power is given as,

  $P=\frac{V^2}{R}$

Where, $V$ is voltage across the bulb and $R$ is resistance of bulb.

Calculation:

From the above relation,

  $R=\frac{V^2}{P}$

So, the resistance of the first bulb,

  $R_1=\frac{{120}^2}{50}=288\Omega$

And the resistance of the second bulb,

  $R_2=\frac{{120}^2}{100}=144\Omega$

Here, $R_1>R_2$

Conclusion:

Therefore, the lower power bulb has higher resistance that is 50 W bulb.