Physics · Class 12 Science
Ch 7Alternating Current — Class 12 Physics, concept-first.
Almost every socket in a home, and every large power station feeding a whole town, ultimately supplies alternating current (AC) rather than the steady, one-directional direct current (DC) that a battery or a cell provides.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
RMS and Peak Value
The root-mean-square value Irms = I₀/√2 of an alternating quantity, equal to the equivalent DC that produces the same heating.
Most relevant Q&A
- Define an alternating current. Write its general sinusoidal form $i=i_0\sin\omega t$ and state clearly what the peak value $i_0$ and the ang…Free
- Define the rms (root-mean-square) value of an alternating current. Starting from $i=i_0\sin\omega t$, derive $I_{rms}=I_0/\sqrt{2}$.Free
- Why do ordinary AC ammeters and voltmeters used in a laboratory record the rms value of an alternating quantity rather than its peak value o…Free
- The peak value of the voltage of a household AC supply is $311\ \text{V}$. Calculate its rms value, and hence state the nominal voltage rati…Free
- An electric lamp is connected to 220 V, 50 Hz supply. Then the peak voltage is (a) 270 V (b) 211 V (c) 311 V (d) 330 VPreview
In previous exams
How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
Almost every socket in a home, and every large power station feeding a whole town, ultimately supplies alternating current (AC) rather than the steady, one-directional direct current (DC) that a batte…
Peak and RMS Values of Alternating Current
Why AC needs a different kind of 'value'. A DC source such as a cell has one fixed voltage at every instant, so quoting 'the voltage' is unambiguous.
Phasors and the Phasor-Diagram Method
Why phasors are needed. When two sinusoidal quantities of the same frequency -- such as an applied voltage and the current it drives -- are not perfectly in step with each other, describing the gap be…
AC Voltage Applied to a Pure Resistor
Setting up the circuit. A pure resistor (with no inductance or capacitance of its own) is connected directly across an AC source supplying .
AC Voltage Applied to a Pure Inductor
Setting up the circuit. A pure inductor (assumed to have no resistance of its own) is connected directly across an AC source supplying .
AC Voltage Applied to a Pure Capacitor
Setting up the circuit. A pure capacitor is connected directly across an AC source supplying .
Reactance and Impedance
Reactance -- the opposition of or alone. Sections 7.5 and 7.6 each produced a relation of the Ohm's-law shape, , for a pure inductor and a pure capacitor respectively.
The LR Series Circuit
Setting up the circuit. A resistor and an inductor are connected in SERIES to an AC source , so the SAME instantaneous current flows through both elements at every instant -- this shared current is th…
The CR Series Circuit
Setting up the circuit. A resistor and a capacitor are connected in SERIES to an AC source , again sharing one common current used as the reference phasor.
The LCR Series Circuit
What changes with all three elements present. A resistor, an inductor and a capacitor connected in one series loop to an AC source share the SAME instantaneous current at every point in the loop -- ex…
Phasor-Diagram Solution for the LCR Circuit
Setting up the phasor diagram. With the current as the common reference phasor, three voltage phasors are drawn from the same origin: along ; perpendicular to , leading it by ; and perpendicular to bu…
Resonance in a Series LCR Circuit
The resonance condition. Section 7.10.1 showed that the impedance of a series LCR circuit is . Since is fixed, is smallest exactly when the term is smallest -- which happens when , making that whole t…
Sharpness of Resonance: Bandwidth and Q-Factor
Defining the bandwidth. The bandwidth of a resonant circuit is defined as the width of the frequency range, centred on , over which the current stays at or above -- equivalently, the range over which…
LC Oscillations (Qualitative Idea)
Setting up the ideal LC circuit. Imagine an inductor and a capacitor connected together in a simple closed loop, with NO resistor and NO external AC source at all -- just the capacitor, initially char…
Power in an AC Circuit: Average Power and Power Factor
Instantaneous power. The instantaneous power delivered to any AC circuit is simply the product of the instantaneous voltage and instantaneous current, .
Wattless Current
Setting up the extreme case. Section 7.13 showed that the average power in a general AC circuit is . Consider the special case of a purely inductive (or purely capacitive) circuit, where exactly.
AC Generator
The basic idea. An AC generator (or alternator) converts mechanical energy into electrical energy by mechanically forcing a coil to rotate inside a magnetic field, using nothing more than Faraday's la…
Transformer
The underlying principle. A transformer changes an alternating voltage from one value to another using mutual induction (Section 6.7 of the previous sub-topic): two separate coils are wound on a commo…
Summary
Peak and rms values. For , the rms value is (similarly for voltage); ordinary AC ratings (e.g. household ) are rms values.
Sample & Board Papers
Sample papers and previous-year board questions for this subject.
+−Show 12 questionsHide questions12 questions
- Q1A series LCR circuit acts as a purely resistive circuit, when (a) wL > 1/wC (b) wL < 1/wC (c) wL = 1/wC (d) none of thesePreview
- Q2A series L-C-R circuit is connected to AC source. Using the phasor diagram, derive the expression for the impedance of the circuit. **OR** T…Preview
- Q3The power factor of L.C.R. circuit at resonance is (a) √2 (b) 1/2 (c) 1 (d) zeroPreview
- Q4An electric lamp is connected to 220 V, 50 Hz supply. Then the peak voltage is (a) 270 V (b) 211 V (c) 311 V (d) 330 VPreview
- Q5Alternating current cannot be measured by D.C. ammeter, because (a) alternating current cannot pass through D.C. ammeter (b) alternating cur…Preview
- Q6(a) Draw a labelled diagram of A.C. generator. [1] (b) Obtain an expression for the instantaneous value of the emf generated in A.C. generat…Preview
- Q7A series LCR circuit fed by an ac source with angular frequency ω acts as a purely resistive circuit, when (a) ωL > 1/ωC (b) ωL < 1/ωC (c) ω…Preview
- Q8Statement I : Direct current (DC) is less dangerous than alternating current (AC). Statement II : The rms value of the alternating current (…Preview
- Q9The equation of an alternating electromotive force is E = 220 sin(100πt − π/15) V, here t is in second. Its rms value and frequency are resp…Preview
- Q10The condition of getting maximum current in an LCR series circuit is (a) X_L = 0 (b) X_C = 0 (c) X_L = X_C (d) R = X_L − X_CPreview
- Q11The ratio of rms value and average value of current for a half cycle of an AC circuit is (a) √2 : π (b) √2 : 1 (c) 2√2 : π (d) π : 2√2Preview
- Q12A transformer carries 4A current in the primary coil of 500 turns. If the input power is 1 kW, what should be the number of turns in the sec…Preview
More questions
32 Q+−Show 10 questionsHide questions10 questions
- Example 1Define an alternating current. Write its general sinusoidal form $i=i_0\sin\omega t$ and state clearly what the peak value $i_0$ and the ang…Free
- Example 2Define the rms (root-mean-square) value of an alternating current. Starting from $i=i_0\sin\omega t$, derive $I_{rms}=I_0/\sqrt{2}$.Free
- Example 3Why do ordinary AC ammeters and voltmeters used in a laboratory record the rms value of an alternating quantity rather than its peak value o…Free
- Example 4What is a phasor? Explain the phasor-diagram method of representing a sinusoidally varying voltage or current, and state what the length and…Preview
- Example 5An AC voltage $v=v_0\sin\omega t$ is applied across a pure resistor $R$. Derive the current through it and show that the voltage and the cur…Preview
- Example 6An AC voltage $v=v_0\sin\omega t$ is applied across a pure inductor $L$. Starting from $v=L\,di/dt$, derive the current through it and show…Preview
- Example 7Define inductive reactance $X_L$. Write its formula and SI unit, and explain how it varies with the frequency of the AC supply.Preview
- Example 8An AC voltage $v=v_0\sin\omega t$ is applied across a pure capacitor $C$. Derive the current through it and show that it leads the voltage b…Preview
- Example 9Define capacitive reactance $X_C$. Write its formula and explain how it varies with frequency, contrasting this behaviour with that of $X_L$…Preview
- Example 10Define the impedance of an AC circuit. For a series LR circuit connected to an AC source, derive the expression for the impedance $Z$ and th…Preview
+−Show 12 questionsHide questions12 questions
- Q11For a series CR circuit connected to an AC source, derive the expression for the impedance $Z$ and the phase angle $\phi$ by which the curre…Free
- Q12A resistor $R$, an inductor $L$ and a capacitor $C$ are connected in series to an AC source $v=v_0\sin\omega t$. Using the phasor-diagram me…Free
- Q13What is meant by resonance in a series LCR circuit? Starting from the impedance formula, derive the expression for the resonant angular freq…Free
- Q14With reference to the current-versus-frequency resonance curve of a series LCR circuit, explain why the current is maximum at resonance, and…Preview
- Q15Define the quality factor (Q-factor) and the bandwidth of a resonant series LCR circuit. Derive the relation $Q=\dfrac{\omega_0 L}{R}$, and…Preview
- Q16Explain qualitatively how an ideal, resistance-free LC circuit, once charged, sustains an electrical oscillation, drawing the analogy with t…Preview
- Q17Derive the expression $P_{avg}=V_{rms}I_{rms}\cos\phi$ for the average power dissipated, over one complete cycle, in a general series AC cir…Preview
- Q18Define power factor. State its value, and hence the average power consumed, for (a) a purely resistive circuit, (b) a purely inductive circu…Preview
- Q19What is meant by a wattless current? Explain why the current flowing in a purely inductive or a purely capacitive AC circuit consumes no pow…Preview
- Q20Describe the construction and working of a simple AC generator, and derive the expression $e=e_0\sin\omega t$ for the emf induced in its rot…Preview
- Q21Explain the underlying principle of a transformer, describe briefly its construction, and derive the turns-ratio relation $V_s/V_p=N_s/N_p$…Preview
- Q22List the main sources of energy loss in a real transformer, and explain briefly how each of them is minimised in practice.Preview
+−Show 10 questionsHide questions10 questions
- Q23The peak value of the voltage of a household AC supply is $311\ \text{V}$. Calculate its rms value, and hence state the nominal voltage rati…Free
- Q24A pure inductor of inductance $0.2\ \text{H}$ is connected across a $230\ \text{V}$ (rms), $50\ \text{Hz}$ AC supply. Calculate (a) the indu…Free
- Q25A pure capacitor of capacitance $15\ \mu\text{F}$ is connected across a $230\ \text{V}$ (rms), $50\ \text{Hz}$ AC supply. Calculate (a) the…Free
- Q26A resistor $R=30\ \Omega$ and an inductor $L=0.1\ \text{H}$ are connected in series to a $200\ \text{V}$ (rms), $50\ \text{Hz}$ AC source. C…Preview
- Q27A resistor $R=40\ \Omega$ and a capacitor $C=100\ \mu\text{F}$ are connected in series to a $200\ \text{V}$ (rms), $50\ \text{Hz}$ AC source…Preview
- Q28A series LCR circuit with $R=100\ \Omega$, $L=0.5\ \text{H}$ and $C=10\ \mu\text{F}$ is connected to a $200\ \text{V}$ (rms), $50\ \text{Hz}…Preview
- Q29A series LCR circuit has $L=1\ \text{H}$, $C=1\ \mu\text{F}$ and $R=10\ \Omega$. Calculate (a) its resonant frequency $f_0$, (b) its quality…Preview
- Q30An AC circuit carries an rms voltage of $200\ \text{V}$ and an rms current of $5\ \text{A}$, with the current lagging the voltage by a phase…Preview
- Q31A rectangular coil of $100$ turns and area $0.1\ \text{m}^2$ rotates with an angular speed of $50\ \text{rad/s}$ in a uniform magnetic field…Preview
- Q32A step-up transformer has $200$ turns in its primary coil and $4000$ turns in its secondary coil. The primary is connected to a $220\ \text{…Preview