Chapter 22, Problem 5STP

To determine

To choose: The correct option.

Answer to Problem 5STP

The correct option is (C), $\text{2}\text{.9}\text{}\times {10}^3\text{ J}$

Explanation of Solution

Given:

A current of 2.0 A is flowing through a motor with resistance $12\Omega$ . The motor is used for duration of one minute.

Formula used:

The energy transformed in a motor, E and with a given resistance value, can be expressed in terms of the power dissipation and the time for which power is drawn, t, as

  $E=Pt$

The power drawn by the motor is a function of its resistance R and current flowing through it, I which can be expressed as,

  $P=I^{2}R$

Calculation:

Substituting the current and resistance value, the power can be obtained as,

  $\begin{array}{c}P=2^2\times 12\\ =48\text{ W}\end{array}$

Now, substituting the value of power and time, the energy can be calculated as,

  $\begin{array}{c}E=48\times 1\times 60\\ =2.88\times {10}^3\text{ W/s}\\ \text{=2}\text{.9}\text{}\times {10}^3\text{ J}\end{array}$

Conclusion:

Therefore, the correct option representing the energy transformed in the resistor is (C), $\text{2}\text{.9}\text{}\times {10}^3\text{ J}$ .