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24 December, 08:07

The current in a series circuit is 19.3 A. When an additional 7.40-Ω resistor is inserted in series, the current drops to 13.4 A. What is the resistance in the original circuit?

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  1. 24 December, 08:14
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    16.8ohms

    Explanation:

    According to ohm's law which states that the current passing through a metallic conductor at constant temperature is directly proportional to the potential difference across its ends.

    Mathematically, V = IRt where;

    V is the voltage across the circuit

    I is the current

    R is the effective resistance

    For a series connected circuit, same current but different voltage flows through the resistors.

    If the initial current in a circuit is 19.3A,

    V = 19.3R ... (1)

    When additional resistance of 7.4-Ω is added and current drops to 13.4A, our voltage in the circuit becomes;

    V = 13.4 (7.4+R) ... (2)

    Note that the initial resistance is added to the additional resistance because they are connected in series.

    Equating the two value of the voltages i. e equation 1 and 2 to get the resistance in the original circuit we will have;

    19.3R = 13.4 (7.4+R)

    19.3R = 99.16+13.4R

    19.3R-13.4R = 99.16

    5.9R = 99.16

    R = 99.16/5.9

    R = 16.8ohms

    The resistance in the original circuit will be 16.8ohms
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