# Formula To Find Total Resistance In A Parallel Circuit

The total resistance of a parallel circuit is calculated by adding the reciprocals of the individual resistances and taking the reciprocal of the resulting sum. This can be expressed mathematically as:

$$R_T = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}$$

where:

* $R_T$ is the total resistance of the parallel circuit * $R_1$, $R_2$, $R_3$, ..., $R_n$ are the individual resistances of the resistors in the parallel circuit

For example, if you have a parallel circuit with three resistors with resistances of 2 ohms, 4 ohms, and 6 ohms, the total resistance of the circuit would be:

$$R_T = \frac{1}{2} + \frac{1}{4} + \frac{1}{6} = \frac{14}{12} = 1.167\ \Omega$$

It is important to note that the total resistance of a parallel circuit is always less than the resistance of any of the individual resistors in the circuit. This is because when resistors are connected in parallel, the current flowing through each resistor is inversely proportional to the resistance of that resistor. This means that the more resistance a resistor has, the less current will flow through it. As a result, the total current flowing through the parallel circuit is greater than the current flowing through any of the individual resistors. This increased current flow results in a lower total resistance for the circuit.

The formula for calculating the total resistance of a parallel circuit can be used to solve a variety of problems involving parallel circuits. For example, you can use the formula to calculate the total resistance of a circuit when you know the resistance of each individual resistor. You can also use the formula to calculate the resistance of a single resistor in a parallel circuit when you know the total resistance of the circuit and the resistances of the other resistors in the circuit.

The formula for calculating the total resistance of a parallel circuit is a simple but powerful tool that can be used to solve a variety of problems involving parallel circuits. By understanding how to use this formula, you can gain a better understanding of how parallel circuits work and how to apply them in real-world applications.

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