What is meant by parallel connection of resistors? Derive the equation for equivalent resistance in a parallel circuit.

(N/A) If the ends of two or more resistors are joined together at common points,such an arrangement is called a parallel connection of resistors.
In a parallel connection,the potential difference $(V)$ remains the same across all resistors,while the total current $(I)$ flowing from the source is divided among the resistors. The sum of the currents flowing through individual resistors is equal to the total current in the circuit.
Consider two resistors $R_{1}$ and $R_{2}$ connected in parallel between points $a$ and $b$,with a battery of terminal voltage $V$ connected across them. The total current $I$ enters at point $a$ and splits into $I_{1}$ and $I_{2}$.
At point $a$,by Kirchhoff's current law:
$I = I_{1} + I_{2}$ ... $(1)$
According to Ohm's law,the current through each resistor is:
$I_{1} = \frac{V}{R_{1}}$ ... $(2)$
$I_{2} = \frac{V}{R_{2}}$ ... $(3)$
Substituting $(2)$ and $(3)$ into $(1)$:
$I = \frac{V}{R_{1}} + \frac{V}{R_{2}} = V \left( \frac{1}{R_{1}} + \frac{1}{R_{2}} \right)$
If $R_{p}$ is the equivalent resistance of the parallel combination,then $I = \frac{V}{R_{p}}$.
Therefore,$\frac{V}{R_{p}} = V \left( \frac{1}{R_{1}} + \frac{1}{R_{2}} \right)$
Thus,the equivalent resistance formula is:
$\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$