How to Calculate Power in a Parallel Circuit

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When resistors are wired in a circuit with a constant voltage, you can calculate the power of the circuit if you know the value of the voltage, in volts, and the values of each resistor, in ohms. Once you have calculated the value of the total resistance of the circuit, you can use Ohm's Law to find the total current, in amperes. You then have all the information you need to calculate the power, which is given by the formula: Power = Current x Voltage.

  • Set up a test circuit with 3 resistors wired in parallel. To obtain a generic formula for this circuit that will work for any values for the voltage and the resistors, call the value of the voltage 'V' and the values of the three resistors 'R1', 'R2' and 'R3'.

  • Use the formula 1/Rt = (1/R1 + 1/R2 + ...1/Rn) to calculate the total resistance of the circuit. For the circuit created in step 1, the total resistance would be 1 / 1/R1 + 1/R2 + 1/R3.

  • Use Ohm's Law to find the current passing through the circuit. Ohm's Law states that the voltage (V) in a circuit is given by multiplying the current (I) by the total resistance (R) of the circuit. This is expressed mathematically as V = IR. If you know the voltage of the circuit and have calculated the total resistance, you can find the current using the formula I = V/Rt.

  • Calculate the power (P) of the circuit in watts by multiplying the voltage and the current. This is expressed mathematically as P = VI. Since the current is dependent on the voltage and resistance, you can simplify the equation by eliminating it and calculating the power from the values of voltage and resistance only. This is expressed mathematically as P = V•V/Rt.

Tips & Warnings

  • For example, if the circuit in step 1 had a voltage of 120-volts and the three resistors wired in parallel had values of 25, 50 and 100 ohms, the power of the circuit would be approximately 1 kw. This is calculated as follows: 1 / Rt = 1 / 25 + 1/ 50 + 1/100 = 7 /100 ohms. Thus Rt = 14.3 ohms and P = 120 x 120 / 14.3 = 1006 watts.
  • The value of a resistor is identified by a series of colored bands marked on the resistor. To find this value, consult a resistor color code table.

References

  • Photo Credit resistor image by naolin from Fotolia.com
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