2E04 H2

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McMaster University *

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2E04

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Electrical Engineering

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May 1, 2024

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docx

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10

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H2 AC Circuit Analysis Short description of the circuit: For this circuit I have included the internal resistance of the inductor as R1 to lower disparity between the results. In this circuit, there is a parallel combination of capacitors and resistors (C1, R2 and C2, R3) in series with the inductor and its internal resistance. Step 1: Solve for the voltage and phase (with respect to the source) at nodes A, B and C, and the current through the inductor analytically. Step 2: Solve the circuit for the same values using MultiSim. Do your results agree with Step 1? Step 3: Recreate the circuit physically and make the necessary measurements, make sure to account for the uncertainties of the measurements. Use the uncertainty values of the Hantek. ANALYTICAL ANALYSIS
My method for solving this analytically will be to convert the source to the phasor form as well as convert the inductors and capacitors to their impedances, then do the necessary equations of parallel and series impedances as well as making use of the voltage divider. Zpar is the impedance value of the parallel combination, and Ztot is the total impedance of the circuit.
We found Vb and Vc using the voltage divider equation, Va is across to the total impedance and Vb is parallel to just Zpar so Vb/Zpar=Va/Ztot. In addition to this we found the magnitude and phase of Vb and Vc as well as the differences in time with respect to the source to help with relating the phases to the MultiSim and the physical measurements. The current through the inductor is dependant on the total inductance of the circuit which was previously found to be slightly inductive which explains the slight lag it has. Table 1 Amplitude Phase(rad) Δt (μs) Va 1.00 V 0 0 Vb 1.72 V -1.218 -110.8 Vc 1.26 V -0.474 -43.1 Il 1.48 mA -0.051 -4.66 Discussion: We can see that we should be seeing Vb, Vc and Il all lag the source voltage. The whole circuit is slightly inductive meaning that the current would be lagging the source voltage. For Vb, the equation we used was Zpar/(Ztot)*Va and Zpar/Ztot was capacitative which means that the voltage would definitely lag the source. However, it can be noticed that Vc lags the source but not as much as Vb because the equation we used was R3/(Zc2+R3) *Vb where R3/(Zc2+R3) has a positive phase which explains why Vc lags the source voltage less.
MULTISIM ANALYSIS Va and Vb shown here with their peak values. Va=999.410 mV Vb=1.660V Va and Vb shown here with their difference in time. ΔT=-109.677 Microseconds.
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