Question

Five resistors are connected purely in parallel to a battery of 24 volts. Three of these resistors are equal and the current through each is I. The current through the fourth resistor is 3.6 times larger than I, and the current through the fifth resistor is 4.7 times smaller than I. What is the power dissipated, in Watts, of the fifth resistor if the equivalent resistance of all five resistors is 13 Ohms?

CORRECT ANSWER IS 26.1!!!!!

Answer 1

V = 24 v

Let the three resistance have resistance x ohm

then current through each of this three resistance

I = V/x

I = 24/x

The current through fourth resistance

I₄ = V/R₄

3.6I = 24/R₄

R₄ = 24/3.6I

R₄ = 6.67/I

R₄ = 6.67 x / 24

R₄ = 0.27 x

The current through fifth resistance

I₅ = V/R₅

I/4.7 = 24/R₅

R₅ = 24 ( 4.7) / I

R₅ = 112.8/I

R₅ = 112.8 x / 24

R₅ = 4.7 x

Equivalent resistance in parallel is given by

x = 89.97 ohm

R₅ = 4.7 x = 4.7 (89.97) = 422.8

Power in fifth resistor will be

P = V² / R₅

P = 24² / 422.8

P = 1.36 W