Chapter 22, Problem 2STP

To determine

To choose: The correct option.

Answer to Problem 2STP

The correct option is (D), $7.3\times {10}^3\text{J}$

Explanation of Solution

Given:

A 5-Ω resistor connected to a 9.0-V battery for duration of 7.5 min.

Formula used:

The energy transformed in a resistor, E 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 resistor is a function of resistance R and voltage drop across it, V ,which can be expressed as,

  $P=\frac{V^2}{R}$

Calculation:

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

  $\begin{array}{c}P=\frac{9^2}{5}\\ =16.2\text{}\text{ W}\end{array}$

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

  $\begin{array}{c}E=16.2\times 7.5\times 60\\ =7.298\times {10}^3\text{ W/s}\\ \text{=7}\text{.3}\text{}\times {10}^3\text{ J}\end{array}$

Conclusion:

Therefore, the correct option representing the energy transformed in the resistor is (D),

  $\text{7}\text{.3}\text{}\times {10}^3\text{ J}$