Question

The electric power varies directly as the square of the voltage () and inversely as the electrical resistance (). If the voltage is 15 volts and the electrical resistance is 3 ohms, then the electric power is 75 watts. Express the electric power as a function of voltage and electrical resistance.

Answer 1

P =
`(V^2)/(R)`

Explanation:

let power be P , voltage V and resistance R

given P varies directly as V² and inversely as R

Then the equation relating them is

P =
`(kV^2)/(R)` ← k is the constant of variation

to find k use the condition V = 15, R = 3 , then P = 75

substitute these values into the equation for P

75 =
`(k(15)^2)/(3)` =
`(225k)/(3)` ( multiply both sides by 3 to clear the fraction )

225 = 225k ( divide both sides by 225 )

1 = k

Then

P =
`(V^2)/(R)`