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AveGali [126]
3 years ago
15

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.
Mathematics
1 answer:
vredina [299]3 years ago
6 0
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.
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