Question

How will a current change if the voltage in a circuit is held constant while the resistance doubles?

Answer 1

Answer:

The current will drop to half of its original value.

Explanation:

To solve this problem, we must use Ohm's law that states that in a circuit the voltage $v$ across a resistor is directly proportional to the current that flows through that circuit. In other words:

$v \propto Ri \\ \\ or: \\ \\ v=Ri \\ \\ It's \ also \ valid: i=\frac{v}{R}$

According to our problem, if the voltage in the circuit is held constant while the resistance double, that is $R_{New}=2R \ and \ v_{New}=v$. So:

$v=R_{New}i_{New} \\ \\ v=2Ri_{New} \\ \\ Isolating \ i_{New}: \\ \\ i_{New}=\frac{v}{2R} \therefore i_{New}=\frac{1}{2}\frac{v}{R} \therefore i_{New}=\frac{1}{2}i$

In conclusion, the current will drop to half of its original value.