An electrical heating element produces heat depending on the resistance of the element and the current passed through it. The he
at 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.
