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10 December, 12:19

Two resistors of 5.0 and 9.0 ohm are connected in parallel. A 4.0 ohm resistor is then connected in series with the parallel combination. A 6.0-V battery is then connected to the series-parallel combination. What is the current through the 5.0 ohm resistor?

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  1. 10 December, 12:39
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    I1 = 0.772 A

    Explanation:

    Given: R1 = 5.0 ohm, R2 = 9.0 ohm, R3 = 4.0 ohm, V = 6.0 Volts

    To find: current I = ? A

    Solution:

    Ohm's law V = I R

    ⇒ I = V / R

    In order to find R (total) we first find R (p) fro parallel combination. so

    1 / R (p) = 1 / R1 + 1 / R2 ∴ (P) stand for parallel

    R (p) = R1R2 / (R1 + R2)

    R (p) = (5.0 * 9.0) / (5.0 + 9.0)

    R (p) = 3.214 ohm

    Now R (total) = R (p) + R3 (as R3 is connected in series)

    R (total) = 3.214 ohm + 4.0 Ohm

    R (total) = 7.214 ohm

    now I (total) = 7.214 ohm / 6.0 Volts

    I (total) = 1.202 A

    This the total current supplied by 6 volts battery.

    as voltage drop across R (p) = V = R (p) * I (total)

    V (p) = 3.214 ohm * 1.202 A = 3.864 volts

    Now current through 5 ohms resister is I1 = V (P) / R1

    I1 = 3.864 volts / 5 ohm

    I1 = 0.772 A
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