Tutorial 7: AC Circuit Analysis Part 2
Course: FAD1022 Basic Physics 2
Semester: 2 2025/2026
Centre: Centre for Foundation Studies in Science, Universiti Malaya (PASUM)
Question 1
A series RLC circuit has resistance $R = 12.0 \Omega$, inductive reactance $X_L = 30.0 \Omega$ and capacitive reactance $X_C = 20 \Omega$. If the RMS voltage across the resistor is 145 V, calculate the:
a) Impedance — ans: 15.62 Ω b) Voltage across inductor — ans: 362.4 V c) Voltage across capacitor — ans: 241.6 V d) Total voltage supplied — ans: 188.73 V e) Average power delivered to the circuit — ans: 1752.12 W f) Reactive power delivered to the circuit — ans: 1459.2 VAr g) Apparent power delivered to the circuit — ans: 2279.37 VA h) Power factor — ans: 0.77 i) Phase angle between voltage and current — ans: 39.76°
Draw phasor diagram between voltage and current and indicate which signal leads.
Question 2
A series AC circuit contains a resistor, an inductor of 1.5 H, a capacitor of $5 \mu\text{F}$ and a generator with 240 V, 50 Hz. The current across the circuit is 0.3 A.
Calculate the:
a) Inductive reactance — ans: 471.24 Ω b) Capacitive reactance — ans: 636.62 Ω c) Impedance — ans: 800 Ω d) Resistance of the circuit — ans: 782.72 Ω e) Average power, reactive power and apparent power delivered to the circuit — ans: 70.45 W, 14.88 VAr, 72 VA f) Power factor — ans: 0.978 g) Phase angle — ans: −10.03°
Draw phasor diagram between voltage and current and indicate which signal leads. Is the circuit more capacitive or inductive?
Question 3
Electrosurgical unit (ESUs) supply high frequency electricity from resonant RLC circuit to cut, coagulate or otherwise modify biological tissue.
Calculate the:
a) Resonant frequency of an ESU with an inductance of $L = 1.25 \mu\text{H}$ and a capacitance of $47.0 \text{ nF}$ — ans: $6.57 \times 10^5$ Hz b) Capacitance required for a resonant frequency of 1.33 MHz if value of inductance does not change — ans: $1.146 \times 10^{-8}$ F c) Phase angle of the ESU at the resonant frequency — ans: $\theta = 0°$ d) Power factor of the ESU at the resonant frequency — ans: PF = 1
Question 4
In an RLC series circuit, the source has an RMS voltage of 120 V, $R = 80.0 \Omega$, and the capacitive reactance is $480 \Omega$. The RMS voltage across the capacitor is 360 V.
Calculate:
a) The current in the circuit — ans: 0.75 A b) The impedance — ans: 160 Ω c) What two values can the reactance of the inductor have? — ans: 618.56 Ω and 341.44 Ω
Question 5
A series RLC circuit is connected to an alternating RMS voltage source of 230 V. The circuit has a power factor of 0.85 and an average power consumption of 800 W.
Calculate the:
a) Impedance of the circuit — ans: 56.32 Ω b) Resistance — ans: 48.87 Ω
Additional Question
A series RLC circuit consists of a resistor ($R=80 \Omega$), an inductor ($L=250\text{mH}$), and a capacitor ($C=10\mu\text{F}$) connected to a variable frequency AC source.
At an unknown frequency, the circuit's impedance is twice the impedance at resonance. Given that the RMS current at resonance is 3 A, determine the resonance frequency and the possible unknown frequency for this condition.
ans: $f_0=100.658 \text{ Hz}$, $f_x = 65.79 \text{ Hz}$ (capacitive circuit) or $154 \text{ Hz}$ (inductive circuit)
Related Concepts
- AC Circuits
- RLC Circuit
- Series RLC Circuit
- Resonance
- Resonant Frequency ($f_0 = \frac{1}{2\pi\sqrt{LC}}$)
- Impedance
- Power Factor ($\cos \phi = \frac{R}{Z}$)
- Average Power ($P_{avg} = I_{rms}^2 R$)
- Reactive Power ($Q = I_{rms}^2 (X_L - X_C)$)
- Apparent Power ($S = V_{rms} I_{rms}$)
- Phase Angle
- Phasor Diagram