How is this formula ( Rt= r1 x r2 / r1 + r2) which is used to calculate total resistance of two parallel resistors found from the formula 1/

Question

How is this formula ( Rt= r1 x r2 / r1 + r2) which is used to calculate total resistance of two parallel resistors found from the formula 1/R1 = 1/r1 +1/r2 ?

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Thanh Hà 4 years 2021-09-05T05:46:16+00:00 1 Answers 13 views 0

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  1. Adela
    0
    2021-09-05T05:47:34+00:00
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    Explanation:

    The total resistance used to calculate the total resistance of the two parallel resistor is given by :

    R_t=\dfrac{r_1\times r_2}{r_1+r_2}

    Taking reciprocal of the above equation.

    \dfrac{1}{R_t}=\dfrac{r_1+r_2}{r_1\times r_2}

    We can also write the above equation as :

    \dfrac{1}{R_t}=\dfrac{r_1}{r_1\times r_2}+\dfrac{r_2}{r_1\times r_2}

    On simplification of above equation,

    \dfrac{1}{R_t}=\dfrac{1}{r_2}+\dfrac{1}{r_1}

    or

    \dfrac{1}{R_t}=\dfrac{1}{r_1}+\dfrac{1}{r_2}

    Hence, proved.

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