Question

A resistor develops 200 J of thermal energy in a time of 10.0s when a current of 1 A is passed through it. If the current is increased to 4 A, what will be the energy (in Joules) developed in 10 s.?

Answer 1

`3200\; {\rm J}`.

Step-by-step explanation:

The power
`P` (rate at which energy is consumed) of an electric circuit is equal to the product of voltage
`V` and current
`I`:

`P = V\, I`.

By Ohm's Law, the current in a resistor is proportional to the voltage in that resistor:

`V = I\, R`,

Where
`R` is the resistance of the resistor.

Substitute the expression for
`V` into the equation for power:

`P = (I\, R)\, I = I^(2)\, R`.

In other words, if resistance stays the same, the rate
`P` at which energy is consumed would be proportional to the square of current.

Hence, when current in this resistor is quadrupled, power consumed would increase to
`4^(2) = 16` times the initial value assuming that resistance stays the same. In the same amount of time, the resistor would now consume:

`16* 200\; {\rm J} = 3200\; {\rm J}`.