Question 1
A 100 Ω resistor is connected to a 220 V, 50 Hz AC supply. Find (a) rms current and (b) average power over a full cycle.
Steps only
Irms=220/100=2.2 A; P=V²/R=220²/100=484 W
Answer
2.2 A; 484 W
CLASS 12 · PHYSICS · CHAPTER 7
Alternating current
Simple worked answers to all 8 current exercises on AC circuits and resonance.
8 worked answersComplete chapter answers
8 worked answers · short steps first, explanations when you need them
Chapter 7 Exercises
Textbook pages 200
Question 2
(a) An AC supply has peak voltage 300 V. Find its rms voltage. (b) An AC current has rms value 10 A. Find its peak value.
Steps only
Vrms=300/√2≈212 V; Ipeak=10√2≈14.1 A
Answer
212 V; 14.1 A
Question 3
A 44 mH inductor is connected to a 220 V, 50 Hz AC supply. Find the rms current.
Steps only
XL=2πfL≈13.82 Ω; I=220/13.82≈15.9 A
Answer
15.9 A
Question 4
A 60 μF capacitor is connected to a 110 V, 60 Hz AC supply. Find the rms current.
Steps only
XC≈44.2 Ω; I=110/44.2≈2.49 A
Answer
2.49 A
Question 5
For Exercises 7.3 and 7.4, find the net power absorbed over a full cycle and explain why.
Steps only
Ideal L and C return stored energy each cycle; average power over a full cycle is zero.
Answer
0 W for each
Question 6
A charged 30 μF capacitor is connected to a 27 mH inductor. Find the angular frequency of free oscillations.
Steps only
ω=1/√(LC)=1/√[(30×10⁻⁶)(27×10⁻³)]≈1.11×10³ rad/s
Answer
1.11×10³ rad/s
Question 7
A series LCR circuit has R=20 Ω, L=1.5 H and C=35 μF and is connected to a 200 V AC source. At its natural frequency, find average power over one cycle.
Steps only
At resonance Z=R=20 Ω; I=200/20=10 A; P=VI=2000 W
Answer
2000 W
Question 8
A series LCR circuit has L=5.0 H, C=80 μF and R=40 Ω, connected to a variable 230 V rms source. Find (a) resonant frequency, (b) impedance and peak current at resonance, and (c) rms voltage drops across R, L and C and show that the LC voltage drops cancel.
Steps only
ω₀=50 rad/s; f₀=7.96 Hz; Z=40 Ω; I₀≈8.13 A; VR=230 V; VL=VC≈1438 V, cancelling
Answer
7.96 Hz; 40 Ω; 8.13 A peak; LC drops cancel