How to Calculate Total Resistance in a Parallel Circuit

A parallel circuit is an electrical circuit in which the components are connected across the same two points, creating multiple paths for current to flow. Unlike a series circuit, the total resistance in a parallel circuit is always less than the smallest individual resistor. Calculating the total resistance is essential in physics, electrical engineering, and electronics because it helps determine the current and voltage distribution within the circuit. Learning how to calculate total resistance in a parallel circuit enables you to analyse and design electrical systems accurately.

1. Table of Contents

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   Identify All the Resistors in the Circuit

Begin by identifying every resistor connected in the parallel circuit.

Record the resistance value of each resistor in ohms (Ω).

• Identify each resistor
• Record the resistance values
• Ensure all values use the same unit

2. Confirm That the Circuit Is Parallel

Check that each resistor is connected across the same voltage source, providing multiple paths for current to flow.

Only use the parallel resistance formula if the circuit is connected in parallel.

• Verify multiple current paths
• Confirm the resistors share the same voltage
• Ensure the circuit is parallel

3. Apply the Parallel Resistance Formula

Use the following formula to calculate the total resistance:

1RT=1R1+1R2+1R3\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}RT​1​=R1​1​+R2​1​+R3​1​

1RT=18+18+18⇒RT=2.67 Ω\frac{1}{R_T}=\frac{1}{\text{8}}+\frac{1}{\text{8}}+\frac{1}{\text{8}}\Rightarrow R_T=\text{2.67}\,\OmegaRT​1​=81​+81​+81​⇒RT​=2.67Ω

IT=VRT=122.67=4.5 AI_T = \frac{V}{R_T} = \frac{\text{12}}{\text{2.67}} = \text{4.5}\,\text{A}IT​=RT​V​=2.6712​=4.5A

R1R_1R1​

Ω

R1R_1R1​

R2R_2R2​

Ω

R2R_2R2​

R3R_3R3​

Ω

R3R_3R3​

VVV

V

VVV

+−R1 = 8 ΩI1 = 1.5 AR2 = 8 ΩI2 = 1.5 AR3 = 8 ΩI3 = 1.5 AI_T = 4.5 AV = 12 V

For example, if you have three resistors with values of 4 Ω, 6 Ω, and 12 Ω, then:

1/RT = 1/4 + 1/6 + 1/12

1/RT = 3/12 + 2/12 + 1/12

1/RT = 6/12 = 1/2

RT = 2 Ω

This means the total resistance of the parallel circuit is 2 Ω.

• Find the reciprocal of each resistance
• Add the reciprocals together
• Find the reciprocal of the final answer

4. Use the Simplified Formula for Two Resistors

If the circuit contains only two resistors, you can use a shorter formula:

RT = (R₁ × R₂) ÷ (R₁ + R₂)

For example, if R₁ = 6 Ω and R₂ = 3 Ω, then:

RT = (6 × 3) ÷ (6 + 3)

RT = 18 ÷ 9 = 2 Ω

• Multiply the two resistances
• Add the two resistances
• Divide the product by the sum

5. Verify Your Answer

After calculating the total resistance, check that the result is lower than the smallest resistor in the circuit.

If it is not, review your calculations because the total resistance in a parallel circuit must always be less than the smallest individual resistance.

• Review your calculations
• Confirm the total resistance is the smallest value
• Correct any errors if necessary

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