A single resistor is connected to a 1.5V battery. The resistor emits 10W of power. What is the resistance of the resistor?

Question

asked Feb 23, 2024 235k views

1 Answer

Jorfus · Answer 1 · 2024-02-27T07:43:32+0000

Answer:

$0.225\; {\rm \Omega}$ (assuming that internal resistance in the battery is negligible.)

Step-by-step explanation:

Let
denote the resistance of this resistor.

Let
denote the voltage across this resistor. In this question, it is given that
$V = 1.5\; {\rm V}$ .

By Ohm's Law, the current
going through this resistor would be equal to:

$\displaystyle I = (V)/(R)$ .

The power
consumed in an electric circuit is equal to the product of voltage and current:

$P = V\, I$ .

Substitute
I = (V / R) into this equation:

$\displaystyle P = (V^(2))/(R)$ .

Rearrange to find resistance
:

$\begin{aligned} R &= (V^(2))/(P) \\ &= \frac{(1.5\; {\rm V})^(2)}{(10\; {\rm W})} \\ &=0.225\; {\rm \Omega}\end{aligned}$ .