Question

As more resistors are added in parallel across a constant voltage source, the power supplied by the source

a. decreases.
b. does not change.
c. increases.

Answer 1

Concepts and reason

The concepts used to solve this question is the resistors in parallel connection and power.

Initially, explain the concept of the resistors in parallel connection and later use the formula of the power delivered by the source to find the correct answer choice.

Fundamentals

In parallel connection of the resistors, the voltage drop across each resistor is the same but the current flowing across each resistor is different.

The equivalent resistance in parallel connection of resistors is calculated as,

$\frac{1}{{{R_P}}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}} + ........ + \frac{1}{{{R_n}}}$

Here, ${R_{\rm{P}}}$ is the equivalent resistance of resistors ${R_1},{R_2},{R_3},.....{R_{\rm{n}}}$ connected in parallel.

The expression for the power delivered by the source is,

$P = \frac{{{V^2}}}{R}$

Here, $P$ is the power delivered by the source, $V$ is the potential difference and $R$ is the resistance.

The equivalent resistance in parallel connection of resistors is calculated as,

$\frac{1}{{{R_P}}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}} + ........ + \frac{1}{{{R_n}}}$

Hence, from the above relation, the equivalent resistance in parallel connection is less than the resistance of the individual resistors.

The expression for the power delivered by the source is,

$P = \frac{{{V^2}}}{R}$

In parallel connection of resisters, the potential difference remains same.

Therefore, from the above relation.

$P \propto \frac{1}{R}$

Hence, the power delivered by the source will increase with a decrease in equivalent resistance of resistors in parallel connection.

Ans:

The power delivered by the source will increase by adding more resistors in parallel connection.