## Parallel Circuits

In electronics, resistors are a crucial component that is used to control the flow of current in a circuit. When two or more resistors are connected in parallel, it is known as a **parallel circuit**. In a parallel circuit, the resistors are connected in such a way that each resistor is connected directly to the power source, and the current is divided among them. In this article, we will explore the concept of resistors in parallel, the parallel resistance formula, and how to calculate the total resistance in a parallel circuit.

A **parallel circuit is** a circuit in which two or more resistors are connected in parallel to a power source. In a parallel circuit, each resistor is connected directly to the power source, and the current is divided among the resistors. A parallel circuit can be represented by a circuit diagram, which is a schematic representation of the circuit that shows the components and their connections.

### Parallel Resistance Formula

The parallel resistance formula is used to calculate the total resistance of a parallel circuit. The formula is as follows:

`1/Rt = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn`

Where Rt is the total resistance, R1, R2, R3, …, and Rn are the individual resistances of each resistor in the circuit.

To use this formula, we must first find the reciprocal of each resistor’s value and add them together. Once we have the sum of the reciprocals, we can find the reciprocal of that sum, which will give us the total resistance of the circuit.

### Total Resistance in a Parallel Circuit

The** total resistance** in a parallel circuit is **less than the resistance of any individual resistor in the circuit**. This is because the current is divided among the resistors, and each resistor offers some resistance to the flow of current. As a result, the total resistance of a parallel circuit is always less than the resistance of any individual resistor in the circuit.

### Calculating the Total Resistance in a Parallel Circuit

To calculate the total resistance in a parallel circuit, we can use the parallel resistance formula. Let’s look at an example to see how it works.

Example:

Suppose we have three resistors connected in parallel to a 12-volt power source. The resistances of the resistors are 2 ohms, 4 ohms, and 6 ohms, respectively. What is the total resistance of the circuit?

Solution:

Using the parallel resistance formula, we can find the total resistance of the circuit as follows:

```
1/Rt = 1/2 + 1/4 + 1/6
1/Rt = (3/6) + (2/6) + (1/6)
1/Rt = 6/6
1/Rt = 1
Rt = 1/1
Rt = 1 ohm
```

Therefore, the total resistance of the parallel circuit is 1 ohm.

### Current in a Parallel Circuit

In a parallel circuit, the current is divided among the resistors based on their individual resistance. The current flowing through each resistor can be calculated using Ohm’s law, which states that the current (I) through a resistor is equal to the voltage (V) across the resistor divided by the resistance (R) of the resistor. The formula is as follows:

`I = V/R`

For example, if a 12-volt power source is connected to three resistors in parallel, and the resistance of the resistors is 2 ohms, 4 ohms, and 6 ohms, respectively, the current flowing through each resistor can be calculated as follows:

```
I1 = 12/2
I1 = 6 amps
I2 = 12/4
I2 = 3 amps
I3 = 12/6
I3 = 2 amps
```

Therefore, the current flowing through the 2-ohm resistor is 6 amps, the current flowing through the 4-ohm resistor is 3 amps, and the current flowing through the 6-ohm resistor is 2 amps.

### Voltage in a Parallel Circuit

In a parallel circuit, the **voltage is the same across all the resistors**. This is because each resistor is connected directly to the power source, and the voltage is the same throughout the circuit.

### Adding Resistors in Parallel

To add resistors in parallel, simply connect them in parallel to the power source. The total resistance of the circuit can be calculated using the parallel resistance formula.

### Parallel Resistor Calculator

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### Conclusion

In conclusion, resistors in parallel are a common component in electronic circuits. In a parallel circuit, the resistors are connected in such a way that each resistor is connected directly to the power source, and the current is divided among them. The total resistance of a parallel circuit is always less than the resistance of any individual resistor in the circuit. The parallel resistance formula is used to calculate the total resistance of a parallel circuit, and the current flowing through each resistor can be calculated using Ohm’s law.

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