Parallel Circuit Analysis: 10 Ohms and 40 Ohms Resistors in a 240V Supply

Understanding the behavior of resistors in parallel circuits is fundamental in electrical engineering. This article will explore a specific scenario where a 10 ohm resistor and a 40 ohm resistor are connected in parallel and supplied with a 240V voltage source. We will calculate the total resistance, the total current flowing through the circuit, and the current flowing through each individual resistor. This analysis is essential for anyone interested in electrical circuits, whether for academic or practical purposes.

Parallel Circuit Basics

Before diving into the specific example, it's important to understand the principles underlying a parallel circuit. In a parallel circuit, the voltage supplies to each component is the same. The total resistance of a parallel circuit can be calculated using specific formulas, which depend on the resistance values of the individual components.

Calculations and Analysis

Step 1: Calculate the Total Resistance

In a parallel circuit, the reciprocal of the total resistance (R_total) is the sum of the reciprocals of the individual resistances. Using the formula:

1/R_total 1/R1 1/R2

Where R1 10 ohms and R2 40 ohms.

Let's calculate:

1/R_total 1/10 1/40 0.1 0.025 0.125 R_total 1 / 0.125 8 ohms

So, the total resistance of the parallel circuit is 8 ohms.

Step 2: Calculate the Total Current in the Circuit

Once we have the total resistance, we can calculate the total current using Ohm's Law (I V / R), where V is the voltage and R is the resistance. Here, V 240V and R_total 8 ohms.

Total current (I_total) 240V / 8 ohms 30 Amps

The total current flowing through the circuit is 30 amperes.

Step 3: Calculate the Current Through Each Resistor

To find the current flowing through each individual resistor, we use Ohm's Law again. Let's calculate the current through the 10 ohm resistor (I1) and the 40 ohm resistor (I2).

For the 10 ohm resistor (I1):

I1 V / R1 240V / 10 ohms 24 Amps

For the 40 ohm resistor (I2):

I2 V / R2 240V / 40 ohms 6 Amps

So, the current flowing through the 10 ohm resistor is 24 amps, and the current flowing through the 40 ohm resistor is 6 amps.

Conclusion

By conducting these calculations, we have gained a comprehensive understanding of how resistors behave in a parallel circuit when supplied with a 240V voltage source. This analysis is crucial for designing and analyzing electrical circuits, ensuring safety and efficiency in various applications.

Frequently Asked Questions (FAQ)

Q1: What is a parallel circuit?

A parallel circuit is an electrical configuration where the components are connected in such a way that the same voltage is applied across them, but the current can take multiple paths.

Q2: How do you calculate the total resistance in a parallel circuit?

The total resistance in a parallel circuit is calculated by taking the reciprocal of the sum of the reciprocals of the individual resistances. The formula is:

1/R_total 1/R1 1/R2 ... 1/Rn

Q3: How do you use Ohm's Law to calculate the current in a circuit?

Ohm's Law states that current (I) is equal to voltage (V) divided by resistance (R). The formula is:

I V / R