How to Find the Current in a Parallel RLC Circuit

Written by david somerset
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A parallel RLC circuit is one that contains one resistor, one inductor and one capacitor all wired in parallel with an AC-voltage source. Since the components are all wired in parallel, the voltage will be the same across each component. Assuming a known ideal resistance, capacitance and inductance, use Ohm's law to calculate the current through each individual component that makes up a parallel RLC circuit.

Skill level:
Easy

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Instructions

  1. 1

    Determine the impedance of the capacitor based on the capacitor's value as well as the frequency of the AC voltage source. The formula for this is "XC = (1/ωC)" where "XC" is the impedance of the capacitor, "ω" is the frequency of the AC voltage source in radians per second and "C" is the capacitor's capacitance value.

  2. 2

    Calculate the impedance of the inductor using the frequency of the AC source and the inductor's value. Use the formula "XL = ωL" where "XL" is the impedance of the inductor, "ω" is the frequency of the AC voltage in radians per second and "L" is the inductance of the inductor.

  3. 3

    Use Ohm's Law to determine the current through each component; the formula is "i = v / XL" for the current through the inductor, "i = v / XC" for the current through the capacitor and "i = v / R" for the resistor's current. Note that "i" is the current value in amps, "v" is the voltage source in volts, "XL" is the capacitor impedance in ohms, "XC" is the capacitor impedance in ohms and "R" is the resistance of the resistor in ohms.

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