# A charge of #36 C# passes through a circuit every #9 s#. If the circuit can generate #40 W# of power, what is the circuit's resistance?

##### 1 Answer

#### Explanation:

The current is

#I = Q/t = frac{36"C"}{9"s"} = 4 "A"#

The power is given by

#P = I^2 R_"eff"# ,

where

#40"W" = (4 "A")^2 R_"eff"#

#R_"eff" = 2.5 Omega#

But where did that formula come from? Read on to find out.

In 1 second, the amount of energy generated is

#1"s" xx 40"W" = 40 "J"#

The amount of charge passing through the resistor is

#frac{36"C"}{9"s"}xx1"s" = 4"C"#

Since

#frac{40"J"}{4"C"} = 10"V"#

And by Ohm's law, we can find the resistance by dividing the potential difference across the resistor by the current passing through it.

#R_"eff" = frac{10"V"}{4"A"} = 2.5 Omega#