# How much power is produced if a voltage of 4 V is applied to a circuit with a resistance of 64 Omega?

Jun 22, 2016

$P = 0.25 W$
*$W$ stands for Watts

#### Explanation:

You have two given quantities:
-Voltage ($V$) and
-Resistance ($R$).

Then we use the following equations:
(1) $V = I R$
and
(2) $P = I V$

we can do solve the problem in two ways:
(A) solve for $I$ and plug it into (2) or (B) we could plug in $I$ from (1) and having the expression:

(3) $P = {V}^{2} / R$

Lets first do (A):

(A.1) $I = \frac{V}{R}$
then lets plug in $V$ and $R$
(A.2) $I = \frac{4 V}{64 \Omega}$
(A.2.1)$I = 0.125 A m p s$
then plug in (A.2.1) in (2)
(A.3) $P = \left(0.125 A m p\right) \cdot \left(4 V\right)$
(A.3.1) $P = 0.25 W$

then (B):
(B.1) $P = {\left(4 V\right)}^{2} / \left(64 \Omega\right) = \frac{16 {V}^{2}}{64 \Omega}$
(B.1.1) $P = 0.25 W$

Hope this helps!