Chapter 22.1, Problem 7PP

To determine

The change in the motor’s power if the potential difference across a motor doubles and the current through the bulb triples.

Answer to Problem 7PP

The power of the motor will become $6$ times of the initial power of the motor.

Explanation of Solution

Given:

The new potential difference across the motor,

  $V\text{'}=2V$

Here, V is the initial potential difference.

The new current through the circuit,

  $I\text{'}=3I$

Here, I is the initial current through the circuit.

Formula used:

The electric power $\left(P\right)$ across a circuit is given by,

  $P=IV$

Where,

Here, I is the current through the circuit and V is the potential difference across it.

Calculation:

Now if the initial power of the motor is,

  $P=IV$

Then, the new electric power of the motor in terms of initial power will be,

  $\begin{array}{c}P\text{'}=I\text{'}V\text{'}\\ =\left(3I\right)\left(2V\right)\\ =6P\end{array}$

Conclusion:

Hence, the electric power of the motor will increase by six times.