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

1 Answer
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 = V/R#
then lets plug in #V# and #R#
(A.2) #I = (4V)/(64Omega)#
(A.2.1)#I = 0.125 Amps#
then plug in (A.2.1) in (2)
(A.3) # P = (0.125 Amp)*(4 V)#
(A.3.1) #P = 0.25W#

then (B):
(B.1) #P = (4V)^2/(64 Omega) = (16V^2)/(64 Omega) #
(B.1.1) #P = 0.25 W#

Hope this helps!