How to Solve Currents for Inductor Circuits

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To calculate the current flowing in series, parallel and series-parallel inductor circuits requires an understanding of some basic electric theory and an understanding of some relatively simple math formulas. Inductors also contain elements of stray capacitance and direct current (DC) resistance but, in most inductors, these elements are negligible and can be disregarded when making calculations of this type. Keep in mind that inductance and inductive reactance is only present when dealing with AC (alternating current) circuits. There is no inductive reactance in a pure DC circuit.

Things You'll Need

  • Pen
  • Paper
  • Calculator
  • Specs sheets

Calculate the Current Flowing in a Series Inductive Circuit

  • Calculate the XL (inductive reactance) for each inductor in the series circuit:

    XL = 2 (Pi) (f) (L) where:
    XL = inductive reactance in ohms
    Pi = 3.1415
    f = frequency in hertz, cps (cycles per second)
    L = inductance in henries (The henry is the basic unit of inductance.)

  • Calculate the total XL of the series circuit:

    XL total = XL1 + XL2 + XL3 + …..

  • Calculate the total series circuit current

    IT = ES/XL total where:
    IT = total current in amperes
    ES = the source voltage (The voltage is applied to the circuit.)

    Since this is a series circuit, the current flowing in any part of the circuit equals the total circuit current.

Calculate the Current Flowing in a Parallel Inductive Circuit

  • Calculate the XL for each inductor.

  • Calculate the total XL for each parallel branch of the circuit. Each branch is considered a series circuit if there is more than one inductance in that branch.

  • Calculate the current flowing in each branch by dividing the source voltage by the total inductive reactance for that branch. Since the same voltage is applied across each branch, the current flowing in any given branch is inversely proportional to its total inductive reactance in ohms.

  • The total circuit current is equal to the sum of the branch currents.

Calculate the Currents Flowing in a Series-Parallel Circuit

  • Calculate the total equivalent inductive reactance for the parallel branches:

    XLeq = 1/XLT = 1/XL1 + 1/XL2 + 1/XL2 + ….

  • Calculate the total XL for the series element.

  • Calculate the total inductive reactance for the circuit by adding the equivalent inductive reactance of the parallel elements with the inductive reactance of the series elements.

  • Divide the circuit source voltage by the circuit's total inductive reactance to get the total current flowing in the circuit.

    For the parallel branches, calculate the individual branch currents as you did before when calculating parallel branch currents.

References

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