Question

question 11 of 25
if the current through a resistor is cut in half, how does the power dissipated by the resistor change? (p = ui = i²r = v²/r)

a. it decreases by a factor of 4.
b. it decreases by a factor of 2.
c. it increases by a factor of 4.
d. it increases by a factor of 2.

Explanation:

Step1: Recall power - current formula

The power dissipated in a resistor is given by $P = I^{2}R$, where $I$ is the current and $R$ is the resistance. Assume the initial current is $I_1$ and the power is $P_1=I_1^{2}R$.

Step2: Calculate new power

The new current $I_2=\frac{I_1}{2}$. Then the new power $P_2 = I_2^{2}R=(\frac{I_1}{2})^{2}R=\frac{I_1^{2}R}{4}$.

Step3: Find the ratio of powers

We find the ratio $\frac{P_2}{P_1}=\frac{\frac{I_1^{2}R}{4}}{I_1^{2}R}=\frac{1}{4}$. So the power decreases by a factor of 4.

Answer:

A. It decreases by a factor of 4.