Question

how does the current in a circuit change if the resistance is doubled?
the current is halved.
the current is doubled.
the current is multiplied by four.
the current stays the same.

Explanation:

Step1: Recall Ohm's Law

Ohm's Law is $V = IR$, where $V$ is voltage, $I$ is current and $R$ is resistance. We can rewrite it as $I=\frac{V}{R}$.

Step2: Consider the new - resistance case

Let the initial resistance be $R_1$ and current be $I_1=\frac{V}{R_1}$. If the resistance is doubled, so $R_2 = 2R_1$. Then the new current $I_2=\frac{V}{R_2}=\frac{V}{2R_1}$.

Step3: Compare the initial and new current

We can see that $I_2=\frac{1}{2}\times\frac{V}{R_1}=\frac{1}{2}I_1$. So the current is halved.

Answer:

The current is halved.