Question

A device of resistance R is connected across a source of V voltage and draws a current I . Derive an expression for power in terms of voltage and resistance

Answer 1

Power = V square/ R...

Answer 2

Explanation:

The mathematical expression from Ohm's law is as follows;

V=IR

Here, I is the current, V is the voltage and R is the resistance.

Rearrange the above expression.

$I=\frac{V}{R}$

The expression for the power in terms of work done and time is as follows;

$P=\frac{W}{t}$

Here, W is the work done and t is the time taken.

Put W= Vq.

$P=\frac{Vq}{t}$

Here, $I= \frac{q}{t}$.

Then, the above expression becomes as,

$P=VI$

The expression for the power in terms of voltage and resistance is as follows;

P= VI

Put $I=\frac{V}{R}$.

$P= V(\frac{V}{R})$

$P= \frac{V^{2}}{R}$

Therefore, the expression for power in terms of voltage and resistance is $P= \frac{V^{2}}{R}$.