On a cold day a battery has a terminal voltage of Vi- 11.96 V and an internal resistance of ri = 0.0095 ? On a warm day the battery has a te

Question

On a cold day a battery has a terminal voltage of Vi- 11.96 V and an internal resistance of ri = 0.0095 ? On a warm day the battery has a terminal voltage of V2-1161 V and an internal resistance of r2 -0.021 2. The device it powers draws the same current at both tempertures. Assume the emf of the battery does not depend on temperature. 33% Part (a) Enter an expression for the current, I, in terms of the given quantities.Part (b) Calculate the cument, I, in amperes. 33% Part (c) what is the battery’s emf, in volts?

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Yến Oanh 4 years 2021-09-05T00:20:34+00:00 1 Answers 18 views 0

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  1. Verity
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    2021-09-05T00:22:26+00:00
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    Answer:

    (a) I = \dfrac{V_1-V_2}{r_2-r_1}

    (b) 29.91 A

    (c) 12.24 V

    Explanation:

    (a) The emf of a battery is the sum of its terminal voltage and lost voltage. The lost voltage is due to the internal resistance. By this, we have for the first condition,

    E = V_1 + Ir_1

    E is the emf, V_1 is the terminal voltage and Ir_1 is the lost voltage with I being the current.

    Since the same current is drawn in both conditions and the emf does not depend on temperature, we have similar for the second condition

    E = V_2 + Ir_2

    Equating both equations and solving for I, we have

    E = V_1 + Ir_1 = V_2 + Ir_2

    I = \dfrac{V_1-V_2}{r_2-r_1}

    (b) Substitute the values from the question into the expression for I in (a)

    I = \dfrac{11.96-11.61}{0.0212-0.0095}=29.91\text{ A}

    (c) Substitute the value of I into any of the equations of E

    E = V_1 + Ir_1

    E = 11.96 + 29.91\times0.0095 = 12.24\text{ V}

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