If a current of #8 A# passing through a circuit generates #14 W# of power, what is the resistance of the circuit?

1 Answer
Jan 13, 2016

The resistance in the circuit will be 0.22 #Omega#

Explanation:

I would combine two laws I have memorised here: Ohm's Law,

#V = IR#

and the Power Law

#P = VI#

I have a current, #I#, of #"8 A"# (ampere) and a power, #P#, of #"14 W"# (watt). I have been asked for a resistance, #R# #Omega# (ohm).

So I want a formula that includes only those three things. If I want to get rid of the #V# in the Power Law, I can replace it with what Ohm's Law says is equal to #V= IR#. So

#P = (IR) * I = I^2 * R#

I need to rearrange to make #R# the subject, so I divide both sides by #I^2# and swap the sides:

#R = P/(I^2) = 14/(8^2) = 14/64 = 0.22 color(white)(a)Omega# (rounded to two decimal places).