# How much power is produced if a voltage of 3 V is applied to a circuit with a resistance of 21 Omega?

Feb 29, 2016

$\frac{3}{7} W$ or $428.571 m W$

#### Explanation:

Let P be power dissipated from 21 ohm resistor to ambient.

Let V be the voltage applied across 21 ohm resistor.

Let I be the current passing through 21 ohm resistor.

We know that power defined as the product of voltage across resistor and current through resistor

Therefore, $P = V I$$- - - - - - \left(1\right)$

By ohm's law, $V = I R$

$\implies I = \frac{V}{R}$$- - - - - - \left(2\right)$

from (1) and (2)

$P = V \times \frac{V}{R}$

$P = {V}^{2} / R$

substitute V=3 volts and R=21 ohms

$\implies P = {3}^{2} / 21$

$\implies P = \frac{9}{21}$

$\implies P = \frac{3}{7}$watts

$\implies P = 0.428571$watts

$\implies P = 428.571 m W$