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19 June, 15:15

You have three identical resistors that you can connect in various ways. Which of the following is NOT a possible value of the equivalent resistance of the three-resistor combinations? A. 3RB. R/3 C. 2R/3D. 3R/2

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  1. 19 June, 16:44
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    Answer: option c.

    Explanation: 3 identical resistors can only have 3 configurations

    1) all 3 resistors in series

    2) all 3 resistors in parallel

    3) 2 parallel resistors in series with 1 resistor.

    Case 1 : all 3 resistors in series

    Let us assume each of the resistor has resistance value R.

    The total resistor (Rt) of 3 resistors in series is given as

    Rt = R1 + R2 + R3

    Since R1=R2=R3=R

    Rt = R+R+R = 3R.

    Case 2: all 3 resistors in parallel.

    The equivalent resistance of resistors in parallel is given by the formulae below.

    1/Rt = 1/R1 + 1/R2 + 1/R3

    Since R1=R2=R3=R

    1/Rt = 1/R + 1/R + 1/R

    1/Rt = 1 + 1 + 1 / R

    1/Rt = 3/R

    3 * Rt = R

    Rt = R/3

    Case 3: 2 parallel resistor in series with one

    First is to get the equivalent resistance of the 2 parallel resistor.

    1/Rt = 1/R1 + 1/R2

    But R1=R2=R

    1/Rt = 1/R + 1/R

    1/Rt = 1 + 1/R

    1/Rt = 2/R

    2 * Rt = R

    Rt = R/2.

    R/2 in series with R has an equivalent resistance as shown below

    Rt = R/2 + R

    Rt = R + 2R/2

    Rt = 3R/2

    Since all the possible 3 configuration are listed above and there is no other then option c (2R/3) is not possible to achieve
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