Rheostat Resistance (Math Problem Sample)

Instructions:

Rheostat Resistance
A 72 Ohm Coil of wire is connected in series with an adjustable Resistor whose Resistance can be varied from 0 to 88 Ohms. if the line Potential of wire is 115 volts, what is the Rheostat resistance when Power taken by the coil is 90 watts?
From ohms law
I=V/R and P = VI
P = V(V/R) = V2R
90 = V2/72
V2 = 90 × 72 = 6480
V = 80.5 Volts
But I = V/R
I = 80.5/72
I = 1.118 Amps
The voltage through this coil is 115 volts and a current of 1.118 Amperes
Therefore, the total Resistance, R = V/I
R = 115/1.118 = 102.86 Ohms
The rheostat resistance = Total resistance – Resistance of the Coil
= 102.86 – 72
= 30.86 Ohms

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