GCSE Physics Tutorial: Calculating Resistance in Parallel

11 Aug

Written By Seb Cox

In parallel circuits, resistors are connected side by side, each having both its positive and negative terminals connected together. Calculating the total resistance in a parallel circuit is more complex than in a series circuit. This tutorial will guide you through the process of calculating resistance in parallel circuits.

1. Understanding Parallel Circuits: In a parallel circuit, each resistor has its own separate path for current flow. The key property of parallel circuits is that the potential difference (voltage) across each resistor is the same, while the current is divided among the parallel branches.

2. Equivalent Resistance (R_eq) for Two Resistors: For two resistors (R₁ and R₂) in parallel, the equivalent resistance (R_eq) is calculated using the formula:

1/R_eq = 1/R₁ + 1/R₂

3. Equivalent Resistance (R_eq) for Multiple Resistors: For multiple resistors (R₁, R₂, R₃, ... Rₙ) in parallel, the equivalent resistance (R_eq) is calculated using the formula:

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ

Or equivalently:

R_eq = 1/(1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ)

4. Steps to Calculate Resistance in Parallel Circuits: Follow these steps to calculate resistance in parallel circuits:

Step 1: Identify the Resistors in Parallel:

Examine the circuit diagram and identify the resistors connected in parallel. Resistors in parallel have both terminal ends connected to each other.

Step 2: Calculate the Inverse of Each Resistor:

Take the inverse of each individual resistance:
```
1/R₁, 1/R₂, 1/R₃, ... 1/Rₙ
```

Step 3: Sum the Inverses:

Add up the inverses of all the resistors:

Sum = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ

Step 4: Calculate the Equivalent Resistance (R_eq):

Take the reciprocal of the sum of the inverses to find the equivalent resistance:
```
R_eq = 1/Sum
```

6. Practical Applications:

Calculating resistance in parallel circuits is fundamental in analysing electrical networks, designing efficient circuits, and understanding the behaviour of complex electrical systems.
It is widely used in electronics, electrical engineering, and household electrical wiring.

7. Summary: Calculating resistance in parallel circuits requires taking the sum of the inverses of individual resistances and then finding the reciprocal of that sum to determine the equivalent resistance. This concept is a vital tool in circuit analysis and design, providing valuable insights into the behaviour of parallel circuits.

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