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17 August, 05:30

How can you connect four of them to produce an equivalent resistance of 0.25 kω?

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  1. 17 August, 06:50
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    Question incomplete

    This is the complete question

    You have a collection of 1.0 kΩ resistors.

    How can you connect four of them to produce an equivalent resistance of 0.25 kΩ?

    Explanation:

    Given that,

    We have collection of resistor

    R = 1.0 kΩ.

    And we want to design an equivalent resistance of

    R = 0.25kΩ

    We know that,

    Series connection of add up resistance and this increases the value of resistance, I. e

    Req = R1 + R2 + R3 + ...

    While

    Parallel resistance add up the reciprocal of resistance and this reduces resistance

    So, 1/Req = 1/R1 + 1/R2 + 1/R3 + ...

    Now, we want to design 0.25kΩ

    Connect four of the resistor in parallel will give a equivalent resistance of 0.25 kΩ

    1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4

    R1 = R2 = R3 = R4 = 1.0 kΩ

    1/Req = 1/1 + 1/1 + 1/1 + 1/1

    1/Req = 1+1+1+1

    1/Req = 4

    Taking reciprocal of both sides ...

    Req = ¼ kΩ

    This is the required equivalent resistance

    So, connect the four of the resistor in parallel will give the required 0.25 kΩ resistance
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