How to Find the Current in a Parallel RLC Circuit Using the Current Divider Rule

Written by jason thompson
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How to Find the Current in a Parallel RLC Circuit Using the Current Divider Rule
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A parallel RLC circuit is comprise of resistors, a capacitor and an inductor arranged parallel to each other. This arrangement means that the circuit has two branches connected separately across the power source. One branch has a resistor and a capacitor, while the other has a resistor and an inductor. As long as you can read the values of the components in the circuit, you can calculate the current anywhere in the circuit.

Skill level:
Moderate

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Instructions

  1. 1

    Multiply the frequency of the current in the circuit (measured in hertz) by 2, and then again by pi (3.14). Multiply this number by the inductance value of the inductor, as measured in Henries. Multiply the result by itself. This is the impedance of the inductor, squared.

  2. 2

    Multiply the value of the resistor that is on the same branch as the inductor, in ohms, by itself. Add this value to the squared impedance of the inductor. Take the square root of the result. This is the impedance of the inductive branch of the circuit.

  3. 3

    Multiply the frequency of the current in the circuit by 2, and then by pi. Multiply this by the capacitance of the capacitor, as measured in farads. Multiply the result by itself. Divide the number 1 by this result. The result will be the impedance of the capacitor, squared.

  4. 4

    Multiply the value of the resistor that is on the same branch as the capacitor, in ohms, by itself. Add this value to the squared value of the capacitor's impedance. Take the square root of the result. This is the impedance of the capacitive branch of the circuit.

  5. 5

    Divide 1 by the impedance of the capacitive branch. This is the inverse capacitive impedance. Divide 1 by the impedance of the inductive branch. This is the inverse inductive impedance. Add the two inverse impedances together. Divide 1 by this number. The result is the equivalent impedance of the whole circuit.

  6. 6

    Divide the voltage powering the circuit by the equivalent impedance. This is the current flowing in the whole circuit. Multiply this by the equivalent impedance, and divide it by the impedance of the capacitive branch, to find the current in the capacitive branch by the current divider rule. Multiply the current in the whole circuit by the equivalent impedance of the circuit and divide the result by the impedance of the inductive branch to find the current flowing in the inductive branch of the circuit, by the current divider rule.

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