How to Calculate a Phase Angle in a Parallel Circuit

By Jason Thompson, eHow Contributor

 
 
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The voltage and current levels of AC circuits vary over time, alternately increasing and decreasing. When the circuit contains capacitors or inductors, the voltage and current do not rise and fall at the same time. Instead, capacitors cause the current to peak before the voltage does. Inductors cause the voltage to peak before the current does. The amount of difference between the two peaks is termed the "phase angle." Though fairly easy to determine for simple series circuits, the calculation of the phase angle of a parallel circuit is much more complex.

Things You'll Need

• Calculator

Instructions

1. • 1
     Add up the capacitance in each branch. To do this, just take the inverse of the capacitance of each capacitor in the branch. Add them together. Take the inverse of the result. This is the capacitance of that branch.
   • 2
     Add up the total inductance of each branch. The inductance of the branch is equal to the sum of the individual inductors in that branch.
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   • 3
     Add up the total resistance of each branch. The resistance of a branch is equal to the sum of the resistances in that branch. Label the resistance of the first branch "R1." Label the resistance of the second branch "R2."
   • 4
     Multiply the capacitance of the first branch by the frequency of the AC signal, and then by 6.28. Take the inverse of the result. This is the capacitive reactance of the first branch. Label this figure "XC1." Determine the capacitive reactance for the second branch and label it "XC2."
   • 5
     Multiply the inductance of the first branch by the frequency of the AC signal and then by 6.28. This is the inductive reactance of that branch. Label it "XL1." Calculate the inductive reactance of the second branch in the same manner and label it "XL2."
   • 6
     Add XC1 and XL1 and label the result "X1." Add XC2 and XL2 and label the result "X2."
   • 7
     Multiply R1 and R2. Label the result "A." Multiply X1 and X2. Label the result "B." Add R1 and R2. Label the result "C." Multiply X1 by R2. Label the result "D." Multiply X2 by R1. Label the result "E." Add X1 and X2. Label the result "F." Subtract B from A. Multiply the result by C. Label this result "G." Add D and E. Multiply the result by F. Label this result "H." Add G and H. Label the result "I." Square C and square F, and add the results together. Label this result "J." Divide I by J. Label this result "Re."
   • 8
     Multiply X1 and R2. Label the result "A." Multiply R1 and X2. Label the result "B." Add R1 and R2. Label the result "C." Multiply R1 by R2. Label the result "D." Multiply X1 by X2. Label the result "E." Add X1 and X2. Label the result "F." Add B to A. Multiply the result by C. Label this result "G." Subtract E from D. Multiply the result by F. Label this result "H." Subtract H from G. Label the result "I." Square C and square F, and add the results together. Label this result "J." Divide I by J. Label this result "Xe."
   • 9
     Divide Xe by Re. Take the inverse tangent of the result. This result is the phase angle of the parallel circuit.