Question

The power, in watts, dissipated as heat in a resistor varies jointly with the resistance, in ohms, and the square of the current, in amperes. A 15-ohm resistor carrying a current of 1 ampere dissipates 15 watts. How much power is dissipated in a 5-ohm resistor carrying a current of 3 amperes?

Answer 1

The power dissipated is 45W.

Explanation:

The power
`P` varies jointly with resistance
`R`, and the square of current
`I`:

`P = \alpha I^2R`,

where
`\alpha` is the constant of proportionality.

Now we are told that when
`R = 15\Omega` and
`I =1A`,
`P = 15W`:

`15 = \alpha (1A)^2*15\Omega`

solving for
`\alpha` we get

`\alpha = 1`,

which gives

`P = I^2R`

With the value of
`\alpha` in hand, we find the power dissipated when
`R =5\Omega` and
`I = 3 A:`

`P = (3A)^2(5\Omega )`

`\boxed{P =45W}`

Thus, the power dissipated is 45W.