## Formula for Power in a Parallel Circuit

In a parallel circuit, the total power dissipated is equal to the sum of the power dissipated by each individual resistor. The formula for power in a parallel circuit is given by: ``` P = V^2 / R ``` where: * P is the power in watts * V is the voltage in volts * R is the resistance in ohms To find the total power dissipated in a parallel circuit, simply add the power dissipated by each resistor: ``` Ptotal = P1 + P2 + P3 + ... + Pn ``` For example, consider a parallel circuit with three resistors, each with a resistance of 10 ohms. The voltage across the circuit is 12 volts. The total power dissipated in the circuit is: ``` Ptotal = (12^2) / 10 = 144 watts ``` The power dissipated by each resistor is: * P1 = (12^2) / 10 = 144 watts * P2 = (12^2) / 10 = 144 watts * P3 = (12^2) / 10 = 144 watts ## Calculating the Voltage in a Parallel Circuit The voltage across each resistor in a parallel circuit is the same. This is because the resistors are connected in parallel, which means that they are all in the same part of the circuit and are therefore subject to the same voltage. The voltage across a resistor in a parallel circuit can be calculated using the following formula: ``` V = IR ``` where: * V is the voltage in volts * I is the current in amps * R is the resistance in ohms For example, consider a parallel circuit with three resistors, each with a resistance of 10 ohms. The current through the circuit is 2 amps. The voltage across each resistor is: ``` V1 = IR1 = (2 amps)(10 ohms) = 20 volts V2 = IR2 = (2 amps)(10 ohms) = 20 volts V3 = IR3 = (2 amps)(10 ohms) = 20 volts ``` ## Calculating the Current in a Parallel Circuit The current through a parallel circuit is not the same in all parts of the circuit. This is because the resistors are connected in parallel, which means that they have different resistances. The current through a resistor in a parallel circuit can be calculated using the following formula: ``` I = V / R ``` where: * I is the current in amps * V is the voltage in volts * R is the resistance in ohms For example, consider a parallel circuit with three resistors, each with a resistance of 10 ohms. The voltage across the circuit is 12 volts. The current through each resistor is: ``` I1 = V1 / R1 = (12 volts) / (10 ohms) = 1.2 amps I2 = V2 / R2 = (12 volts) / (10 ohms) = 1.2 amps I3 = V3 / R3 = (12 volts) / (10 ohms) = 1.2 amps ``` ## Calculating the Resistance in a Parallel Circuit The resistance of a parallel circuit is less than the resistance of any of the individual resistors. This is because the resistors are connected in parallel, which means that they are all in the same part of the circuit and are therefore subject to the same current. The resistance of a resistor in a parallel circuit can be calculated using the following formula: ``` 1 / R = 1 / R1 + 1 / R2 + 1 / R3 + ... + 1 / Rn ``` where: * R is the total resistance in ohms * R1, R2, R3, ..., Rn are the individual resistances in ohms For example, consider a parallel circuit with three resistors, each with a resistance of 10 ohms. The total resistance of the circuit is: ``` 1 / R = 1 / 10 ohms + 1 / 10 ohms + 1 / 10 ohms = 3 / 10 ohms R = 10 / 3 ohms = 3.33 ohms ``` ## Conclusion The formula for power in a parallel circuit is P = V^2 / R. The voltage across each resistor in a parallel circuit is the sameSeries And Parallel Circuits Sparkfun Learn

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