Question

State the law of the combination of resistances in parallels.

Answer 1

Concept Used: Law of Parallel Connection of Resistances

Step 1: Parallel Combination of resistances:

The law of the combination of resistances in parallel states that," when two or more resistances are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of all the individual resistances."

Thus, if R₁, R₂, R₃, etc., are combined in parallel then, the equivalent (resultant) resistance (R) is given by

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

Step 2: Derivation:

From Ohm's law, the total current flowing through the circuit is given by,

$$\begin{gathered} I=\frac{V}{R} \\ I=I_1+I_2+I_3 \\ \frac{V}{R}=\frac{V}{R_1}+\frac{V}{R_2}+\frac{V}{R_3} \\ \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} \end{gathered}$$

This relationship gives the equivalent resistance for a parallel combination of the resistances R₁, R₂, and R₃. Thus, for a parallel combination of resistances,

Reciprocal of the equivalent resistance = Sum of reciprocals of all the individual