Explanation:
The total resistance used to calculate the total resistance of the two parallel resistor is given by :
[tex]R_t=\dfrac{r_1\times r_2}{r_1+r_2}[/tex]
Taking reciprocal of the above equation.
[tex]\dfrac{1}{R_t}=\dfrac{r_1+r_2}{r_1\times r_2}[/tex]
We can also write the above equation as :
[tex]\dfrac{1}{R_t}=\dfrac{r_1}{r_1\times r_2}+\dfrac{r_2}{r_1\times r_2}[/tex]
On simplification of above equation,
[tex]\dfrac{1}{R_t}=\dfrac{1}{r_2}+\dfrac{1}{r_1}[/tex]
or
[tex]\dfrac{1}{R_t}=\dfrac{1}{r_1}+\dfrac{1}{r_2}[/tex]
Hence, proved.
