Chapter 22.2, Problem 30PP

To determine

Time required to accomplish the task.

Answer to Problem 30PP

  $t\text{'}=1.1$ hour

Explanation of Solution

Given:

Initial voltage rating of water heater, $V=120\text{V}$

Time taken to heat, $t$

New voltage rating of water heater, $V\text{'}=240\text{V}$

Current is same, $I\text{'}=I$

Energy required is same $E\text{'}=E$

Formula Used:

The energy power relation is given as,

  $E=Pt=VIt$

Where, $E$ is energy, $P$ is power, $V$ is voltage and $t$ is time.

Calculation:

Let, the energy required for 120 V unit is

  $\begin{array}{l}E=VIt\\ \Rightarrow t=\frac{E}{VI}=\frac{E}{120\times I}\end{array}$

So energy required for 240 V unit is

  $\begin{array}{l}E\text{'}=V\text{'}I\text{'}t\text{'}\\ \Rightarrow t\text{'}=\frac{E\text{'}}{V\text{'}I\text{'}}=\frac{E}{240\times I}\\ \Rightarrow t\text{'}=\frac{t}{2}\left(\text{Since }t=\frac{E}{120\times I}\right)\\ \Rightarrow t\text{'}=\frac{2.2}{2}=1.1\text{hour}\end{array}$

Conclusion:

Therefore, the time required to accomplish the same task is 1.1 hours.