## Formula for Total Resistance in a Parallel Circuit

In a parallel circuit, the total resistance is calculated by adding the reciprocals of the individual resistances and then taking the reciprocal of the result. This can be expressed mathematically as follows: ``` Rt = 1 / (1 / R1 + 1 / R2 + ... + 1 / Rn) ``` where: *### Rt

is the total resistance of the parallel circuit *### R1

,### R2

, ...,### Rn

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: ``` Rt = 1 / (1 / 2 + 1 / 4 + 1 / 6) = 1 / (0.5 + 0.25 + 0.1667) = 1 / 0.9167 = 1.09 ohms ``` It is important to note that the total resistance of a parallel circuit is always less than the smallest resistance in the circuit. This is because in a parallel circuit, the current is divided among the different resistors. The more resistors there are in the circuit, the more the current is divided, and the lower the total resistance will be. ## Calculating the Current in a Parallel Circuit The current in a parallel circuit can be calculated by 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 1.09 ohms and a voltage of 12 volts, the current in the circuit would be: ``` I = 12 V / 1.09 ohms = 11.01 amps ``` ## Calculating the Voltage across a Resistor in a Parallel Circuit The voltage across a resistor in a parallel circuit can be calculated by using the following formula: ``` V = I * R ``` where: *### V

is the voltage across the resistor *### I

is the current in the circuit *### R

is the resistance of the resistor For example, if you have a resistor with a resistance of 2 ohms in a parallel circuit with a total resistance of 1.09 ohms and a current of 11.01 amps, the voltage across the resistor would be: ``` V = 11.01 amps * 2 ohms = 22.02 volts ``` ## Calculating the Power Dissipated by a Resistor in a Parallel Circuit The power dissipated by a resistor in a parallel circuit can be calculated by using the following formula: ``` P = I^2 * R ``` where: *### P

is the power dissipated by the resistor *### I

is the current in the circuit *### R

is the resistance of the resistor For example, if you have a resistor with a resistance of 2 ohms in a parallel circuit with a total resistance of 1.09 ohms and a current of 11.01 amps, the power dissipated by the resistor would be: ``` P = (11.01 amps)^2 * 2 ohms = 242.4 watts ``` ## Summary The formula for total resistance in a parallel circuit is: ``` Rt = 1 / (1 / R1 + 1 / R2 + ... + 1 / Rn) ``` The current in a parallel circuit can be calculated by using the following formula: ``` I = V / Rt ``` The voltage across a resistor in a parallel circuit can be calculated by using the following formula: ``` V = I * R ``` The power dissipated by a resistor in a parallel circuit can be calculated by using the following formula: ``` P = I^2 * R ```Virp Table Archives Regents Physics

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