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 ?

Answer 1

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.