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

a) It remains the same b) It increases by a factor of 2 c) It decreases by a factor of 2 d) It increases by a factor of 4 Answer: d) It increases by a factor of 4.

Step-by-step solution

Write down the power formula

Power (P) = I^2 * R

Calculate the initial power

Let the initial current be I and resistance be R. Initial Power (P1) = I^2 * R

Calculate the new power when current is doubled

When the current is doubled, it becomes 2I. Now, we'll find the new power (P2). New Power (P2) = (2I)^2 * R

Compare the initial power and new power

We have P1 = I^2 * R and P2 = (2I)^2 * R. Now let's divide P2 by P1: P2/P1 = ((2I)^2 * R) / (I^2 * R) P2/P1 = (4 * I^2 * R) / (I^2 * R) P2/P1 = 4 The new power is 4 times the initial power.

Select the correct option

The power dissipated is increased by a factor of 4, so the correct answer is option d) It increases by a factor of 4.