Series and Parallel AC Circuits

A quantity sometimes used in DC circuits is conductance, symbolized by the letter G. Conductance is the reciprocal of resistance (G = ¹/_R), and it is measured in the unit of siemens.

Expressing the values of resistors in terms of conductance instead of resistance has certain benefits in parallel circuits. Whereas resistances (R) add in series and “diminish” in parallel (with a somewhat complex equation), conductances (G) add in parallel and “diminish” in series. Thus, doing the math for series circuits is easier using resistance and doing math for parallel circuits is easier using conductance:

In AC circuits, we also have reciprocal quantities to reactance (X) and impedance (Z). The reciprocal of reactance is called susceptance (B = ¹/_X), and the reciprocal of impedance is called admittance (Y = ¹/_Z). Like conductance, both these reciprocal quantities are measured in units of siemens.

Write an equation that solves for the admittance (Y) of this parallel circuit. The equation need not solve for the phase angle between voltage and current, but merely provide a scalar figure for admittance (in siemens):

Calculate the total impedance offered by these three resistors to a sinusoidal signal with a frequency of 10 kHz:

R₁ = 3.3 kΩ

R₂ = 10 kΩ

R₃ = 5 kΩ

State your answer in the form of a scalar number (not complex), but calculate it using two different strategies:

Calculate total resistance (R_total) first, then total impedance (Z_total).

Calculate individual admittances first (Y_R1, Y_R2, and Y_R3), then total impedance (Z_total).

Calculate the total impedance offered by these three capacitors to a sinusoidal signal with a frequency of 4 kHz:

C₁ = 0.1 μF

C₂ = 0.047 μF

C₃ = 0.033 μF

State your answer in the form of a scalar number (not complex), but calculate it using two different strategies:

Calculate total capacitance (C_total) first, then total impedance (Z_total).

Calculate individual admittances first (Y_C1, Y_C2, and Y_C3), then total impedance (Z_total).