Three identical resistors, when connected in series, transform electrical energy into thermal energy at a rate of 12 W (4.0 W per resistor).

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.

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King 3 years 2021-09-04T06:44:39+00:00 2 Answers 0 views 0

Answers ( )

  1. Adela
    0
    2021-09-04T06:45:39+00:00
    Reply

    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.

  2. hongcuc2
    0
    2021-09-04T06:45:41+00:00
    Reply

    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

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