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24 September, 10:57

A battery has emf E and internal resistance r = 1.50 Ω. A 14.0 Ω resistor is connected to the battery, and the resistor consumes electrical power at a rate of 92.0 J/s. What is the emf of the battery?

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  1. 24 September, 11:09
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    E = 39.68 V

    Explanation:

    EMF (Electromotive force) : This is defined as the magnitude of the potential difference of both the external circuit and the inside of the cell. The S. I unit is Volt.

    The Expression for E. M. F is given as,

    E = I (R+r) ... Equation 1

    Where E = EMF, I = current, R = External Resistance, r = internal resistance.

    Also,

    P = I²R

    I = √ (P/R) ... Equation 2

    Where P = power, R = External resistance.

    Given: P = 92 J/s, R = 14 Ω.

    Substitute into equation 2

    I = √ (92/14)

    I = √ (6.57)

    I = 2.56 A.

    Also Given: r = 1.5 Ω.

    Substitute into equation 1

    E = 2.56 (1.5+14)

    E = 2.56 (15.5)

    E = 39.68 V.
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