Please help !!! A 12 V battery is set up in an unknown configuration. The internal resistance of the battery is 4 Ohms. If this circuit must

Question

Please help !!! A 12 V battery is set up in an unknown configuration. The internal resistance of the battery is 4 Ohms. If this circuit must have a minimum of two resistors, what resistance must these resistors have and what configuration must they be in in order for a terminal voltage to read 11.478 V? Show all work

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Delwyn 2 months 2021-08-02T08:50:52+00:00 1 Answers 2 views 0

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  1. hongcuc2
    0
    2021-08-02T08:52:14+00:00
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    Answer:

    Explanation:

    Given that,

    Battery capacity

    E=12V

    Internal resistance of battery r=4ohms

    We are told that the circuit must have at least 2 resistor

    If the terminal voltage is Vt= 11.478V

    Let all the resistor we want to connect the battery have a equivalent resistance Req

    Req = R1 +R2 + R3+…+ Rn

    Series connection

    Using KVL in the circuit,

    E = I(R+r)

    12 = I ( Req + 4) equation 1

    When the terminal voltage is 11.478V, I.e voltage across the external resistance, in this case the equivalent resistance Req

    Using ohms law

    Vt=I•Req

    Then,

    11.478 = I•Req equation 2

    Make I subject of formulae

    Then, I = 11.478/Req. Equation 3

    Substitute equation 3 into 1

    12 = I ( Req + 4)

    12 = 11.478/Req ( Rea + 4)

    12 = 11.478 + 45.912/Req

    12 – 11.478 = 45.912/Req

    0.522 = 45.912/Req

    Cross mutilply

    0.522 Req = 45.912

    Then, Req = 45.912/0.522

    Req = 87.95 ohms

    Req ≈ 88 ohms

    The resistor must have a resistance of 88 ohms and they have a series configuration

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