Question

With the help of suitable diagram derive equivalent resistance of resistors in parallel combination.

Answer 1

Let us make a circuit as shown in following diagram. Let us assume that three resistors $R_1,R_2$ and $R_3$ are in parallel combination. Currents $I_1,I_2$ and $I_3$ are flowing respectively through $R_1,R_2$ and $R_3.$ Potential difference in the circuit is V and current through the circuit is I.
As per Ohm's Law:
Current through $R_1$ is $I_1=\frac{V}{R_1}$

Current through $R_2$ is $I_2=\frac{V}{R_2}$

Current through $R_3$ is $I_3=\frac{V}{R_3}$
And current through the circuit is $I=\frac{V}{R}$ where R is equivalent resistance

Using above equations, we get
$I=I_1+I_2+I_3$

or, $I=\frac{V}{R_1}+\frac{V}{R_2}+\frac{V}{R_3}$

or, $I=v(\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3})$
this means that;

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$