Question

If the current through a resistor is increased by a factor of \(2,\) how does this affect the power that is dissipated? a) It decreases by a factor of 4 . b) It increases by a factor of 2 . c) It decreases by a factor of 8 . d) It increases by a factor of 4 .

Short answer

Answer: d) It increases by a factor of 4.

Step-by-step solution

Identify given values and the power formula

The current through the resistor is increased by a factor of 2, so we can represent the new current as 2I. We need to use the formula for power dissipation in a resistor, P = I^2R, to find the effect on power dissipation.

Calculate the initial power

Using the power formula P = I^2R, we can calculate the initial power dissipation in the resistor. Let's call this P1. P1 = I^2R.

Calculate the new power

Now, we need to calculate the new power dissipation when the current is increased by a factor of 2 (2I). Let's call this P2. P2 = (2I)^2R = 4I^2R.

Find the ratio of new power to initial power

To find how the power dissipation is affected, we need to find the ratio of the new power (P2) to the initial power (P1). Ratio = P2/P1 = (4I^2R) / (I^2R) = 4.

Match the result with the provided options

From our calculation, we find that the power dissipation increases by a factor of 4 when the current is increased by a factor of 2. This matches option (d). So, the correct answer is d) It increases by a factor of 4.