Question

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

Answer 1

The current will drop to half of its original value.

Step-by-step 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=(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)=(v)/(2R) \therefore i_(New)=(1)/(2)(v)/(R) \therefore i_(New)=(1)/(2)i`

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