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Parallel Circuit Analysis: Calculating Current Through a Resistor

February 27, 2025Technology3859
Parallel Circuit Analysis: Calculating Current Through a Resistor When

Parallel Circuit Analysis: Calculating Current Through a Resistor

When working with electrical circuits, one common task is to determine the current flowing through a specific resistor. This is particularly straightforward in a parallel circuit. In this article, we will delve into the steps involved in calculating the current through a particular resistor in a simple parallel circuit. We will use a practical example to illustrate the process.

Understanding the Circuit

Consider a circuit that has a 9.0A current source and three resistors of equal magnitude (5 ohms each) connected in parallel. Our goal is to find the current in the third resistor. Let's first understand the key principles involved.

Total Resistance in a Parallel Circuit

The formula for calculating the total resistance in a parallel circuit is given by:

[frac{1}{R_{text{total}}} frac{1}{R_1} frac{1}{R_2} frac{1}{R_3}]

Given that (R_1 R_2 R_3 5Omega), we can substitute the values into the equation:

[frac{1}{R_{text{total}}} frac{1}{5} frac{1}{5} frac{1}{5} frac{3}{5}]

Therefore, the total resistance (R_{text{total}}) is:

[R_{text{total}} frac{5}{3} Omega approx 1.67 Omega]

Total Current in the Circuit

The total current (I_{text{total}}) flowing through the circuit is given as 9.0A. Using Ohm's Law, we can find the voltage across the total resistance:

[V I_{text{total}} times R_{text{total}} 9.0 text{A} times frac{5}{3} Omega 15 text{V}]

This means each resistor in the parallel circuit is subjected to a voltage of 15V.

Current Through Each Resistor

Using Ohm's Law again, we can find the current through each resistor:

[I_n frac{V}{R_n} frac{15 text{V}}{5 Omega} 3 text{A}]

Since all resistors are identical, the current through the third resistor (R_3) is also 3A.

Alternative Explanation

Kirchhoff's Current Law (KCL) states that the sum of currents entering a node is equal to the sum of currents leaving the node. In a parallel circuit, this means the current is divided equally among all parallel branches.

Given that the resistors are identical and there are three of them, the total current of 9.0A is divided equally:

[frac{9.0 text{A}}{3} 3 text{A}]

Thus, the current through the third resistor is 3.0A.

Conclusion

In a parallel circuit with identical resistors, the current is evenly distributed. This numerical and theoretical approach ensures that you can accurately determine the current through any specific resistor.