Question

An electric circuit with a 115V source consists of a 72 ohms fixed resistor that is connected in series to a variable resistor with X ohms. if the circuit delivers 90 watts of power, determine the resistance of the variable resistor

Answer 1

In this question, let’s consider the image below:

For two resistors connected in series, the effective resistance can be given by the sum of the two resistors.

We can take the resistance offered by the rheostat to be x ohms.

The total resistance becomes (x+72) ohms.

The current through the circuit can be obtained by:

P = VI

I = P/V

I = 90/115 = 0.7826A

The power can also be given as:

P = 90 =  I²R.

P = 90 = (0.7826²) (x+72)

P = 90 = 0.6125(x+72)

P = 0.6125x + 44.1

90 = 0.6125x +44.1

45.9 = 0.6125x

We divide by 0.6125 on both sides to determine the value of x

45.9/0.6125 = 75

 

X= 75 ohms

the resistance of the variable resistor (rheostat) is 75 ohms