resistors in series and parallel

When resistors are connected in series, their equivalent resistance

${𝑅}_{\text{eq}}$ can be calculated using the formula:

${𝑅}_{\text{eq}}={𝑅}_1+{𝑅}_2+{𝑅}_3+\dots$

Where ${𝑅}_1,{𝑅}_2,{𝑅}_3,\dots$ are the resistances of individual resistors.

In series configuration, the resistors are connected end-to-end, creating a single path for the current to flow. As a result, the same current flows through each resistor, while the total voltage across the series combination is the sum of the voltages across each resistor.

In the diagram below, resistors ${𝑅}_1,{𝑅}_2,$ and ${𝑅}_3$ are connected in series:

To determine the equivalent resistance of the series combination, the resistances of all the resistors are simply added together to find ${𝑅}_{\text{eq}}$.

${𝑅}_{\text{eq}}={𝑅}_1+{𝑅}_2+{𝑅}_3$

This formula holds true for any number of resistors connected in series. When resistors are in series, the equivalent resistance is always equal to the sum of the individual resistances.

When resistors are connected in parallel, their equivalent resistance ${𝑅}_{\text{eq}}$ can be calculated using the formula:

Resistor in Paralllel for 2 Resitors 

$\frac{1}{{𝑅}_{\text{eq}}}=\frac{1}{{𝑅}_1}+\frac{1}{{𝑅}_2}+\frac{1}{{𝑅}_3}+\dots$

Where ${𝑅}_1,{𝑅}_2,{𝑅}_3,\dots$ are the resistances of individual resistors.

In parallel configuration, each resistor is connected across the same voltage source, creating multiple current paths. As a result, the total current flowing through the parallel combination is the sum of the currents flowing through each resistor. However, the voltage across each resistor remains the same.

In the diagram below, resistors ${𝑅}_1,{𝑅}_2,$ and ${𝑅}_3$ are connected in parallel:

To determine the equivalent resistance of the parallel combination, the reciprocal of each resistor's value is summed, and then the reciprocal of the total is taken to find ${𝑅}_{\text{eq}}$.

${𝑅}_{\text{eq}}=\frac{1}{\frac{1}{{𝑅}_1}+\frac{1}{{𝑅}_2}+\frac{1}{{𝑅}_3}}$

This formula is applicable to any number of resistors connected in parallel. When resistors are in parallel, the equivalent resistance is always less than the smallest resistance in the combination.