Question

The current in a circuit is halved. What happens to the resistance?

V=IR

(1 point)
Responses

The resistance stays the same.
The resistance stays the same.

The resistance is tripled.
The resistance is tripled.

The resistance is doubled.
The resistance is doubled.

The resistance is halved.

Answer 1

According to Ohm's Law, \( V = IR \), where \( V \) is voltage, \( I \) is current, and \( R \) is resistance. If the current \( I \) is halved and the voltage \( V \) remains constant, the resistance \( R \) must change to maintain the equation.

If we denote the original current as \( I_0 \) and the new current as \( I_1 = \frac{1}{2} I_0 \), we can rearrange Ohm's Law to find resistance.

Given that:
\[ R = \frac{V}{I} \]

If the current is halved and the voltage remains the same:
- Original resistance: \( R_0 = \frac{V}{I_0} \)
- New resistance when current is halved: \( R_1 = \frac{V}{I_1} = \frac{V}{\frac{1}{2} I_0} = \frac{2V}{I_0} = 2R_0 \)

Thus, if the current is halved, the resistance is doubled.

The correct response is:
**The resistance is doubled.**