Asingle resistor is connected across the terminals of a battery. which one or more of the following changes in voltage and current leaves unchanged the electric power dissipated in the resistor? (a) doubling the voltage and reducing the current by a factor of two. (b) doubling the voltage and increasing the resistance by a factor of four. (c) doubling the current and reducing the resistance by a factor of four.

All of the choices are correct

Explanation:

The power dissipated in a single resistor connected to a battery is given by:

where

V is the voltage

I is the current

R is the resistance

Let's analyze each case:

A) Doubling the voltage (V'=2V) and reducing the current by a factor of 2 (I'=I/2). The new power dissipated is:

--> the power is unchanged

B) Doubling the voltage (V'=2V) and increasing the resistance by a factor of 4 (R'=4R). The new power dissipated is:

--> the power is unchanged

C) Doubling the current (I'=2I) and reducing the resistance by a factor of four (R'=R/4). The new power dissipated is:

--> the power is unchanged