What is the primary purpose of calculating equivalent resistance?

The primary purpose of calculating equivalent resistance is to simplify complex electrical circuits. By replacing a network of multiple resistors with a single equivalent resistor, we can easily determine the total current drawn from the power source using Ohm's Law ($V = I R_{eq}$). This simplification makes it much easier to analyze the overall circuit behavior before delving into the specifics of current and voltage distribution within the original, more intricate resistor network.

When are resistors considered to be in series?

Resistors are considered to be in series when they are connected end-to-end, forming a single, uninterrupted path for the electric current. This means that the same current flows through each resistor in the series combination. There are no branching points between them. The total voltage across the series combination is the sum of the individual voltage drops across each resistor.

When are resistors considered to be in parallel?

Resistors are considered to be in parallel when their terminals are connected to the same two common points in the circuit. This arrangement ensures that the potential difference (voltage) across each resistor in the parallel combination is identical. The total current entering the parallel combination divides among the individual branches, with the sum of the branch currents equaling the total current.

Can equivalent resistance ever be zero or infinite?

Yes, equivalent resistance can be zero or effectively infinite. If a perfect conductor (a wire with zero resistance) is connected in parallel with any resistor, the equivalent resistance of that parallel combination becomes zero, effectively 'short-circuiting' the resistor. Conversely, if a resistor is part of an open circuit (a break in the path), the resistance of that path is considered infinite, meaning no current can flow through it.

How does equivalent resistance relate to power dissipation in a circuit?

Equivalent resistance helps in calculating the total power dissipated by the entire resistor network. Once $R_{eq}$ is found, the total power dissipated by the circuit can be calculated using $P_{total} = V_{total} I_{total} = I_{total}^2 R_{eq} = rac{V_{total}^2}{R_{eq}}$. This total power is the sum of the power dissipated by each individual resistor in the original network, providing a holistic view of energy conversion within the circuit.

Equivalent Resistance

Physics

NEET UG

Version 1Updated 22 Mar 2026

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Equivalent resistance, denoted as $R_{eq}$ , is the single hypothetical resistance that, when connected across the same two points in a circuit, would draw the exact same total current from the source as the original combination of resistors, given the same applied potential difference. It effectively simplifies a complex network of resistors into a single, manageable component for analysis. This c…

Quick Summary

Equivalent resistance ( $R_{eq}$ ) is a conceptual single resistor that can replace a network of multiple resistors while maintaining the same total current flow from the source for a given potential difference.

This simplification is vital for analyzing complex circuits. For resistors connected in series, the current is the same through each, and the total voltage is the sum of individual voltage drops. The equivalent resistance is the direct sum of individual resistances: $R_{eq} = R_1 + R_2 + ...

+ R_n $. For resistors connected in parallel, the voltage across each is the same, and the total current is the sum of individual branch currents. The reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances:$ rac{1}{R_{eq}} = rac{1}{R_1} + rac{1}{R_2} + ...

+ rac{1}{R_n} $. A common shortcut for two parallel resistors is$ R_{eq} = rac{R_1 R_2}{R_1 + R_2}$. Understanding these combinations is fundamental to solving circuit problems, including those involving mixed series-parallel arrangements and special cases like the Wheatstone bridge.

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Key Concepts

Resistors in Series

When resistors are connected in series, they are arranged sequentially, one after another, so that the…

Resistors in Parallel

In a parallel connection, resistors are connected across the same two points in a circuit, creating multiple…

Mixed Combinations and Circuit Reduction

Most practical circuits involve a combination of series and parallel connections. To find the equivalent…

Series: —

R_{eq} = R_1 + R_2 + ... + R_n

(Current same, Voltage divides)

Parallel: —

rac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}

(Voltage same, Current divides)

Two Parallel Resistors: —

R_{eq} = \frac{R_1 R_2}{R_1 + R_2}

n Identical Resistors (R) in Series: —

R_{eq} = nR

n Identical Resistors (R) in Parallel: —

R_{eq} = \frac{R}{n}

Wheatstone Bridge Balanced: —

rac{R_1}{R_2} = \frac{R_3}{R_4}

(Middle arm ignored)

Same Current, Add Resistance (Series) Parallel Voltage, Reciprocal Resistance (Parallel)