Tutorial 6: AC Circuit Analysis
Course: FAD1022 Basic Physics 2
Semester: 2 2025/2026
Centre: Centre for Foundation Studies in Science, Universiti Malaya (PASUM)
Question 1
A capacitor has an RMS current of 21 mA at a frequency of 60 Hz when the RMS voltage across it is 14 V.
Calculate:
a) The capacitance of the capacitor. b) If the frequency is increased, will the current in the capacitor increase, decrease or stay the same? Explain. c) Calculate the RMS current in the capacitor at a frequency of 410 Hz.
Question 2
An RMS voltage of 12.2 V with a frequency of 1.00 kHz is applied to a 0.290 mH inductor.
Calculate:
a) The RMS current in the circuit. b) Determine the peak current for a frequency of 2.50 kHz.
Question 3
A resistor of resistance $R = 20 \Omega$ and an inductor of inductance $L = 0.15 \text{ H}$ is connected in series to a sinusoidal AC source of RMS voltage 200 V. At a frequency of 50 Hz, calculate the:
a) inductive reactance of the inductor. b) Impedance of the circuit. c) RMS current across the circuit. d) phase angle of the circuit.
Draw the phasor diagram of voltage and current. State which signal leads.
Question 4
A 200 V, 5 kHz AC supply is connected to a series circuit consisting of a resistor and a capacitor. The circuit is designed such that the phase angle between the source voltage and the current is $-45°$.
Given:
- Circuit current is 2 A
Calculate:
a) The values of resistor, capacitive reactance and impedance. b) The capacitance of the capacitor. c) If the supply frequency is doubled to 10 kHz, analyse how this will affect the:
- i) Capacitive reactance
- ii) Impedance
- iii) Circuit current
- iv) Phase angle
Provide calculations and explain the implications of these changes.
Question 5
A black box circuit contains an unknown resistor and an unknown inductor, connected in series to a 250 V, 400 Hz AC source. The total circuit current, voltage across the resistor and voltage across the inductor is 2.5 A, 150 V and 200 V, respectively.
Calculate:
a) The values of resistor and inductor. b) The phase angle of the circuit. c) Draw phasor diagram for current and voltage.
Additional Questions
Question A1
An AC circuit having a frequency of 500 Hz has a RMS current value of 30 mA.
Calculate:
a) If a $35 \Omega$ resistor is connected across the circuit, compute the RMS voltage across the resistor. b) If a $4.0 \mu\text{F}$ capacitor is connected across the circuit, compute the reactance and the RMS voltage across the capacitor. c) If a $5.0 \text{ mH}$ inductor is connected across the circuit, compute the reactance and the RMS voltage across the inductor.
Question A2
A 120 V, 5 kHz AC source is connected to two different circuits:
Circuit A (RL Series): A resistor $R=100 \Omega$ is in series with an inductor $L=10\text{mH}$.
Circuit B (RC Series): The same resistor $R=100 \Omega$ is in series with a capacitor $C=1\mu\text{F}$.
Determine for both circuits:
a) Inductive reactance and capacitive reactance. b) Impedance for each circuit. c) Current flowing through each circuit. d) Phase angle for each circuit.
Compare the parameters above in both circuits. Which circuit causes the current to lead, and which circuit causes the current to lag? Draw the phasor diagram for each case.
Related Concepts
- AC Circuits
- AC Circuit
- Capacitive Reactance ($X_C = \frac{1}{2\pi f C}$)
- Inductive Reactance ($X_L = 2\pi f L$)
- Impedance ($Z = \sqrt{R^2 + (X_L - X_C)^2}$)
- Phase Angle ($\tan \phi = \frac{X_L - X_C}{R}$)
- Phasor Diagram
- RL Circuit
- RC Circuit
- Reactance