Question
The current in a circuit is halved. What happens to the resistance?
V=IR
(1 point)
Responses
The resistance is doubled.
The resistance is doubled.
The resistance stays the same.
The resistance stays the same.
The resistance is halved.
The resistance is halved.
The resistance is tripled.
V=IR
(1 point)
Responses
The resistance is doubled.
The resistance is doubled.
The resistance stays the same.
The resistance stays the same.
The resistance is halved.
The resistance is halved.
The resistance is tripled.
Answers
GPT-4o mini
According to Ohm's Law, which states that \( V = IR \) (where \( V \) is voltage, \( I \) is current, and \( R \) is resistance), if the current (\( I \)) in a circuit is halved and the voltage (\( V \)) remains constant, the resistance (\( R \)) must increase.
To see why, you can rearrange the equation to find resistance: \( R = \frac{V}{I} \). If \( I \) is halved (let’s say it changes from \( I \) to \( \frac{I}{2} \)), then plugging this into the formula gives:
\[
R_{\text{new}} = \frac{V}{\frac{I}{2}} = \frac{2V}{I} = 2R_{\text{old}}
\]
Thus, the resistance is doubled.
The correct response is:
**The resistance is doubled.**
To see why, you can rearrange the equation to find resistance: \( R = \frac{V}{I} \). If \( I \) is halved (let’s say it changes from \( I \) to \( \frac{I}{2} \)), then plugging this into the formula gives:
\[
R_{\text{new}} = \frac{V}{\frac{I}{2}} = \frac{2V}{I} = 2R_{\text{old}}
\]
Thus, the resistance is doubled.
The correct response is:
**The resistance is doubled.**