Question

question 21 of 25
the potential difference across a resistor increases by a factor of 2. how does the current change? (ohms law: v = ir)
a. it decreases by a factor of 2.
b. it decreases by a factor of 4.
c. it increases by a factor of 4.
d. it increases by a factor of 2.

Explanation:

Step1: Write Ohm's law

$V = IR$, so $I=\frac{V}{R}$.

Step2: Consider the new - situation

Let the initial potential difference be $V_1$ and the initial current be $I_1=\frac{V_1}{R}$. The new potential difference $V_2 = 2V_1$. Since the resistance $R$ is constant, the new current $I_2=\frac{V_2}{R}=\frac{2V_1}{R}$.

Step3: Find the ratio of new and old currents

$\frac{I_2}{I_1}=\frac{\frac{2V_1}{R}}{\frac{V_1}{R}} = 2$. So $I_2 = 2I_1$.

Answer:

D. It increases by a factor of 2.