When resistors 1 and 2 are connected in series, the equivalent resistance is 20.4 Ω. When they are connected in parallel, the equivalent res

Question

When resistors 1 and 2 are connected in series, the equivalent resistance is 20.4 Ω. When they are connected in parallel, the equivalent resistance is 3.86 Ω. What are (a) the smaller resistance and (b) the larger resistance of these two resistors?

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Thu Giang 5 years 2021-08-04T14:11:17+00:00 1 Answers 174 views 0

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  1. binhan
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    2021-08-04T14:12:23+00:00
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    Answer:

    (A) Smaller resistance will be equal to 5.175 ohm

    (b) Larger resistance will be equal to 15.225 ohm  

    Explanation:

    Let the two resistances are R_1 and R_2

    It is given that when they are connected in series their equivalent resistance is 20.4 ohm

    So R_!+R_2=20.4——eqn 1

    When they are connected in parallel their equivalent resistance is  3.86 ohm

    So \frac{R_!R_2}{R_1+R_2}=3.86

    From equation 1

    R_1R_2=3.86\times 20.4=78.744

    R_1-R_2=\sqrt{(R_1+R_2)^2-4R_!R_2}=\sqrt{(20.4)^2-4\times 78.744}=10.05 ……eqn 2

    Adding eqn 1 and eqn 2

    2R_1=30.45

    R_1=15.225ohm putting this value in eqn 1

    R_2=20.4-15.225=5.175ohm

    (a) Smaller resistance will be equal to 5.175 ohm

    (b) Larger resistance will be equal to 15.225 ohm

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