An electrical heating element produces heat depending on the resistance of the element and the current passed through it. The heat produced can be given by the formula h = I2R where h is the heat generated, I is the current, and R is the resistance. If the element has a fixed current of 2 amps passing through it and a variable current of x amps, it is able to produce a heat of 10x3 + 80, depending on the variable resistance for different additional values of current x. Determine the formula for the variable resistance.

The heat produced by current I is

H = I²R

where

R = resistance.

According to the formula, heat produced is proportional to the square of the current.

When a current of I = 2 amps is applied, the heat produced is

H = 10x³ + 80.

This heat includes heat due to a fixed current of 2 amps, and heat due to a variable current of x amps.

Because the heat produced is proportional to the square of the current, write the expressions as

H = (10x) * (x²) + 20 * (2²)

The second term on the right is heat due to the fixed current of 2 amps, written as

20 * (2²).

Therefore the fixed resistance is R = 20 ohms, and the square of the fixed current is 2².

The first term represents heat due to variable resistance, written as

(10x) * (x²).

Therefore the variable resistance is 10x, and the square of the variable current is x².

Answer:

The variable current is 10x.