Alternating Current is a core and high-weightage chapter in Class 12 Physics that explains the behavior of AC circuits used in real-life electrical systems. This chapter covers important topics such as AC voltage and current, RMS and average values, reactance, impedance, LCR series circuits, resonance, power factor, wattless current, and transformers, which are frequently asked in CBSE board exams and competitive exams like JEE and NEET.
NCERT Solutions for Class 12 Physics Chapter 7 – Alternating Current are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are explained in simple, step-by-step language with clear derivations, phasor diagrams, and solved numericals, helping students build strong conceptual clarity, practise numericals effectively, and score well in board examinations.
NCERT Solutions for Class 12 Physics Chapter 7 – Alternating Current
Q.
A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.
(a) What is the rms value of current in the circuit?
(b) What is the net power consumed over a full cycle?
Q.
An LC circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t =0.
(a) What is the total energy stored initially? Is it conserved during LC oscillations?
(b) What is the natural frequency of the circuit?
(c) At what time is the energy stored?
(i) Completely electrical (i.e., stored in the capacitor)?
(ii) Completely magnetic (i.e., stored in the inductor)?
(d) At what times is the total energy shared equally between the inductor and the capacitor?
(e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?
Q.
A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is 0.5 Ω per km. The town gets power from the line through a 4000-220 V step-down transformer at a sub-station in the town.
(a) Estimate the line power loss in the form of heat.
(b) How much power must the plant supply, assuming there is negligible power loss due to leakage?
(c) Characterise the step up transformer at the plant.
Q.
Answer the following questions:
(a) In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for rms voltage?
(b) A capacitor is used in the primary circuit of an induction coil.
(c) An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.
(d) A choke coil in series with a lamp is connected to a dc line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp’s brightness. Predict the corresponding observations if the connection is to an ac line.
(e) Why is choke coil needed in the use of fluorescent tubes with ac mains? Why can we not use an ordinary resistor instead of the choke coil?
Q.
A series LCR circuit with L = 0.12 H, C = 480 nF, R = 23 Ω is connected to a 230 V variable frequency supply.
(a) What is the source frequency for which current amplitude is maximum. Obtain this maximum value.
(b) What is the source frequency for which average power absorbed by the circuit is maximum. Obtain the value of this maximum power.
(c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?
(d) What is the Q-factor of the given circuit?
Q.
A circuit containing a 80 mH inductor and a 60 μF capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible.
(a) Obtain the current amplitude and rms values.
(b) Obtain the rms values of potential drops across each element.
(c) What is the average power transferred to the inductor?
(d) What is the average power transferred to the capacitor?
(e) What is the total average power absorbed by the circuit? [‘Average’ implies ‘averaged over one cycle’.]
Q.
Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements, L, C and R are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified in Exercise 7.11 for this frequency.
Q.
A 100 μF capacitor in series with a 40 Ω resistance is connected to a 110 V, 60 Hz supply.
(a) What is the maximum current in the circuit?
(b) What is the time lag between the current maximum and the voltage maximum?
Q.
A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V, 50 Hz ac supply.
(a) What is the maximum current in the coil?
(b) What is the time lag between the voltage maximum and the current maximum?
Q.
Figure 7.21 shows a series LCR circuit connected to a variable frequency 230 V source. L= 5.0 H, C = 80μF, R = 40 Ω
(a) Determine the source frequency which drives the circuit in resonance.
(b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
(c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.
Q.
(a) The peak voltage of an ac supply is 300 V. What is the rms voltage?
(b) The rms value of current in an ac circuit is 10 A. What is the peak current?
Q.
A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200 μH, what must be the range of its variable capacitor?
[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radiowave.]
Q.
A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 μF is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
Q.
Suppose the initial charge on the capacitor in Exercise 7.7 is 6 mC. What is the total energy stored in the circuit initially? What is the total energy at later time?
Q.
A charged 30 μF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?
Q.
Obtain the resonant frequency ωr of a series LCR circuit with L = 2.0 H, C = 32 μF and R = 10 Ω. What is the Q-value of this circuit?
Q.
In Exercises 7.3 and 7.4, what is the net power absorbed by each circuit over a complete cycle. Explain your answer.
Q.
A 60 μF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.
Q.
A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.
Q.
Do the same exercise as above with the replacement of the earlier transformer by a 40,000-220 V step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred?
NCERT Solutions for Class 12 Physics Chapter 7 – Alternating Current
Q. 1) Answer the following questions:
(a) In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for rms voltage?
(b) A capacitor is used in the primary circuit of an induction coil.
(c) An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.
(d) A choke coil in series with a lamp is connected to a dc line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp’s brightness. Predict the corresponding observations if the connection is to an ac line.
(e) Why is choke coil needed in the use of fluorescent tubes with ac mains? Why can we not use an ordinary resistor instead of the choke coil?
Ans:
(a) Yes; the statement is not true for rms voltage.
It is true that in any ac circuit, the applied instantaneous voltage is equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit. But, this is not true for rms voltage because such voltages across different elements may not be in same phase.
(b) The capacitor is used in the primary circuit of an induction coil. This is because, when a circuit is broken, a high induced voltage is used to charge the capacitor to avoid sparking.
(c) The dc signal will appear across capacitor C because for dc signals, the impedance of an inductor (L) is very low while the impedance of a capacitor (C) is very high (almost infinite). The capacitor blocks the dc signal. Therefore, a dc signal appears across C. For an ac signal of high frequency, the impedance of L is high and that of C is negligible. The inductor blocks the ac signal of high frequency. Therefore, an ac signal of high frequency appears across L.
(d) On a dc line, choke offers no impedance. Therefore, the lamp shines brightly and the insertion of an iron core in the choke causes no change in the lamp’s brightness.
However, on an ac line, both the choke coil and the iron core increase the impedance of the circuit. Therefore, if an iron core is inserted in the choke coil (which is in series with a lamp connected to the ac line), the lamp will glow dimly.
(e) A choke coil is needed in the use of fluorescent tubes with ac mains because it reduces ac across the tube without much loss of power. We cannot use an ordinary resistor instead of a choke coil for this purpose because it wastes power in the form of heat.
Note: Q&A containing MathML or Latex or Katex code cannot be rendered in pdf document.
FAQs: Class 12 Physics Chapter 7 – Alternating Current
Q1. Is Alternating Current important for exams?
Yes, it is a high-weightage chapter for CBSE, JEE, and NEET.
Q2. Which topics are most important in this chapter?
RMS value, LCR circuits, resonance, power factor, and transformers.
Q3. Are numericals asked from this chapter?
Yes, LCR circuit and power-based numericals are very common.
Q4. Are derivations important here?
Yes, derivations of impedance, resonance condition, and transformer equations are frequently asked.
Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with solved numericals and diagrams.