Question

Three identical resistors, when connected in series, transform electrical energy into thermal energy at a rate of 12 W (4.0 W per resistor). Part A Determine the power consumed by the resistors when connected in parallel to the same potential difference. Express your answer with the appropriate units.

Answer 1

Answer:

108 Watts

Explanation:

The total circuit resistance when the resistors are connected in series is

               R + R + R = 3R

When he resistors are connected in parallel, the resistance reduces from 3R in the series circuit to become;

             $\frac{1}{R} + \frac{1}{R} + \frac{1}{R}$

                   = $\frac{R}{3}$ Ω

$Power = \frac{V^{2}}{R}$

The voltage supply was given to be constant for both the series and parallel circuits. This implies that V² is constant and power is inversely proportional to resistance.

Therefore;

Power for the parallel connected circuit = $\frac{3R}{\frac{R}{3} } * 12 W$

                            = 9 × 12 W = 108 Watts

Answer 2

Answer:

Explanation:

Potential difference, V and let each resistance, R

Resistors are in series, total resistance, Rₓ = R1 + R2 + R3

= R + R + R

= 3R

Power, P = V²/Rₓ

12 = V²/3R

V²/R = 36

Resistors are in parallel, total resistance, 1/Rₓ = 1/R1 + 1/R2 + 1/R3

Rₓ = R/3

P = V²/Rₓ

P = V²/(R/3)

P = 3(V²/R)

= 3(36)

= 108 W.