# Calculating Total Resistance Parallel Circuit

## Calculating Total Resistance in a Parallel Circuit

In a parallel circuit, the total resistance is less than the resistance of any individual resistor. This is because the current can flow through multiple paths, so each resistor has a smaller share of the total current. The total resistance of a parallel circuit can be calculated using the following formula: ``` Rt = 1 / (1/R1 + 1/R2 + ... + 1/Rn) ``` where: *

### Rt

is the total resistance of the circuit *

,

, ...,

### Rn

are the resistances of the individual resistors For example, if you have a circuit with three resistors of 10 ohms, 20 ohms, and 30 ohms, the total resistance would be: ``` Rt = 1 / (1/10 + 1/20 + 1/30) = 5 ohms ``` It is important to note that the total resistance of a parallel circuit is always less than the resistance of the smallest resistor in the circuit. This is because the smallest resistor has the largest current flowing through it, which means that it has the greatest effect on the total resistance of the circuit. ## Calculating Current in a Parallel Circuit The current in a parallel circuit is the same in all branches of the circuit. This is because the voltage across all branches of the circuit is the same, and the current is inversely proportional to the resistance. The current in a parallel circuit can be calculated using the following formula: ``` I = V / Rt ``` where: *

### I

is the current in the circuit *

### V

is the voltage across the circuit *

### Rt

is the total resistance of the circuit For example, if you have a parallel circuit with a total resistance of 5 ohms and a voltage of 12 volts, the current in the circuit would be: ``` I = 12 volts / 5 ohms = 2.4 amps ``` ## Calculating Voltage in a Parallel Circuit The voltage across a parallel circuit is the same in all branches of the circuit. This is because the current is the same in all branches of the circuit, and the voltage is directly proportional to the current. The voltage across a parallel circuit can be calculated using the following formula: ``` V = IRt ``` where: *

### V

is the voltage across the circuit *

### I

is the current in the circuit *

### Rt

is the total resistance of the circuit For example, if you have a parallel circuit with a total resistance of 5 ohms and a current of 2.4 amps, the voltage across the circuit would be: ``` V = 2.4 amps * 5 ohms = 12 volts ``` ## Power in a Parallel Circuit The power in a parallel circuit is the product of the current and the voltage. The power in a parallel circuit can be calculated using the following formula: ``` P = IV ``` where: *

### P

is the power in the circuit *

### I

is the current in the circuit *

### V

is the voltage across the circuit For example, if you have a parallel circuit with a current of 2.4 amps and a voltage of 12 volts, the power in the circuit would be: ``` P = 2.4 amps * 12 volts = 28.8 watts ``` ## Summary To summarize, the total resistance of a parallel circuit is less than the resistance of any individual resistor in the circuit. The current in a parallel circuit is the same in all branches of the circuit. The voltage across a parallel circuit is the same in all branches of the circuit. The power in a parallel circuit is the product of the current and the voltage.

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