Table of contents

27. Resistors & DC Circuits

Power in Circuits

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Multiple Choice

A certain resistor is connected across a $9.0 V$ battery and dissipates $20 W$ of power. The battery is replaced with an $18 V$ battery. How much power is dissipated in the resistor now?

5 . 0 W

10 W

20 W

40 W

60 W

80 W

Verified step by step guidance

First, understand the relationship between voltage, resistance, and power. The power dissipated by a resistor can be calculated using the formula:

P_{1} = \frac{{V_{1}}^{2}}{R}

, where

V_{1}

is the initial voltage and

R

is the resistance.

Given that the initial power

P_{1}

is 20 W and the initial voltage

V_{1}

is 9 V, use the formula to find the resistance

R

R = \frac{{V_{1}}^{2}}{P_{1}}

Calculate the resistance

R

using the values:

R = \frac{9^{2}}{20}

. This will give you the resistance in ohms.

Now, replace the battery with an 18 V battery. Use the power formula again to find the new power

P_{2}

P_{2} = \frac{{V_{2}}^{2}}{R}

, where

V_{2}

is 18 V.

Substitute the values into the formula:

P_{2} = \frac{18^{2}}{R}

. Calculate the new power dissipated by the resistor using the resistance found earlier.

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A certain resistor is connected across a 9.0 V battery and dissipates 20⁢ W of power. The battery is replaced with an 18 V battery. How much power is dissipated in the resistor now?