Chapter 24, Problem 106A

To determine

The change in power in a circuit with a corresponding increase in current.

Answer to Problem 106A

The change in power is $120\text{ W}$.

Explanation of Solution

Given:

The current in a 120-V circuit increases from 1.3 A to 2.3 A.

Formula used:

The power drawn by a circuit is a function of current I and voltage drop across it, V, which can be expressed as,

  $P=VI$

Calculation:

The supply voltage of the circuit is 120-V and the current is initially 1.3 A. The power drawn by the circuit under this condition is,

  $\begin{array}{c}P=120\times 1.3\\ =156\text{ W}\end{array}$

In the second case, the current is increased to 2.3 A with the same supply voltage. The power drawn by the circuit in this case is,

  $\begin{array}{c}{P}_{new}=120\times 2.3\\ =276\text{ W}\end{array}$

Thus, the increase in the power can be calculated as,

  $\begin{array}{c}\Delta P=P_{new}-P\\ =276-156\\ =120\text{ W}\end{array}$

Conclusion:

The change in power for the given increase is 120 W and the power has increased from the initial value.