Multiple Choice & Assertion-Reason

PHYExam Practice

This is a chapter-wide rapid-revision article covering the one-mark MCQ and Assertion-Reason traps across electromagnetic induction and AC. The recurring ideas are Lenz's law sign, flux units, peak-vs-RMS conversions, phase in pure $L$ and $C$ , series-LCR resonance, wattless power and transformer/inductance scaling.

Examiners use these to test the conceptual clarity that the numericals assume.

Faraday-Lenz law

\varepsilon = -N\,\dfrac{d\phi}{dt}

\varepsilon

= induced EMF (V),

N

= number of turns,

\phi

= flux per turn (Wb); the minus sign is Lenz's law (the EMF opposes the change in flux).

RMS value of sinusoidal AC

I_{rms} = \dfrac{I_0}{\sqrt{2}}, \qquad V_{rms} = \dfrac{V_0}{\sqrt{2}}

I_0, V_0

= peak (amplitude) values; valid only for a sinusoid.

Impedance & resonance (series LCR)

Z = \sqrt{R^2 + (X_L - X_C)^2}, \qquad X_L = X_C \Rightarrow Z = R

X_L = \omega L

X_C = 1/\omega C

; at resonance the net reactance is zero so

Z

is minimum (

=R

) and the current is maximum.

Average power

P_{av} = V_{rms} I_{rms} \cos\phi

\cos\phi

= power factor; for a pure

L

or pure

C

\phi = 90^{\circ}

P_{av} = 0

(wattless).

Ideal transformer & self-inductance scaling

\dfrac{V_s}{V_p} = \dfrac{N_s}{N_p} = \dfrac{I_p}{I_s}, \qquad L \propto N^2

step-up has

N_s > N_p

(more turns, larger voltage, smaller current); the

L

of a solenoid scales as

N^2

Lenz's law: the induced current always OPPOSES the change in flux that produces it — this is a statement of energy conservation and is the source of the minus sign in Faraday's law.
SI unit of magnetic flux is the weber (Wb); $1\,\text{Wb} = 1\,\text{T}\cdot\text{m}^2$ . Tesla is the unit of $B$ , henry of inductance, farad of capacitance.
Peak-to-RMS: for $I_0 = 4\,\text{A}$ , $I_{rms} = 4/\sqrt{2} = 2\sqrt{2}\,\text{A} \approx 2.83\,\text{A}$ — never divide by 2.
In a pure inductor the current LAGS the voltage by $90^{\circ}$ ; in a pure capacitor the current LEADS by $90^{\circ}$ (mnemonic CIVIL: in C, I leads V; V leads I in L).
At series-LCR resonance $Z = R$ (minimum), current is maximum, and the circuit behaves purely resistively with power factor 1.
Power in a pure reactance is zero averaged over a cycle because $\cos 90^{\circ} = 0$ ; energy is stored and returned, not dissipated.
Eddy currents in a transformer core are reduced by laminating the core (thin insulated sheets raise the resistance of eddy-current paths); a solid core would make them worse.
Self-inductance of a solenoid $\propto N^2$ (not $N$ ), since both the flux per turn and the number of linkages scale with $N$ .

Where the marks go

Dividing the peak value by 2 instead of $\sqrt{2}$ to get the RMS value (or vice versa).
Swapping the lead/lag in pure $L$ and pure $C$ — remember current lags in $L$ , leads in $C$ .
Claiming a pure inductor or capacitor dissipates power; its average power is zero (wattless) — only $R$ dissipates.
In Assertion-Reason items on resonance, both Assertion and Reason can be true with the Reason correctly explaining the Assertion, since $X_L = X_C \Rightarrow Z = R$ gives maximum current.

How the board asks it

Assertion–Reasonlenz's law as a statement of energy conservation
Assertion (A): The induced current in a closed loop always opposes the change in magnetic flux that produces it. Reason (R): Lenz's law is a direct consequence of the conservation of energy. Select the correct option: (a) both A and R true and R is the correct explanation of A; (b) both true but R not the correct explanation; (c) A true, R false; (d) A false, R true.
Assertion–Reasonseries-lcr resonance $X_L = X_C \Rightarrow Z = R$
Assertion (A): At resonance, a series $LCR$ circuit carries the maximum possible current. Reason (R): At resonance $X_L = X_C$ , so the impedance reduces to $Z = R$ , its minimum value. Choose the correct option from (a)-(d) regarding the truth of A, R and whether R correctly explains A.
Assertion–Reasonwattless power; $\cos 90^\circ = 0$ in a pure reactance
Assertion (A): A pure inductor connected across an AC source dissipates no power averaged over a complete cycle. Reason (R): The phase difference between voltage and current in a pure inductor is $90^\circ$ , so the average power $P = V_{rms} I_{rms}\cos\phi$ is zero. Select the correct option (a)-(d).
Assertion–Reasonphase in pure $C$ (CIVIL mnemonic): current leads by $90^\circ$
Assertion (A): In a purely capacitive AC circuit the current leads the voltage by $90^\circ$ . Reason (R): In a pure capacitor the current and the applied voltage are in phase. Decide the truth values and whether R explains A, choosing from (a)-(d).
Assertion–Reasoneddy-current losses reduced by laminating the transformer core
Assertion (A): The core of a transformer is made of thin laminated sheets rather than a solid block. Reason (R): Lamination increases the resistance of the eddy-current paths, thereby reducing eddy-current power losses in the core. Select the correct option from (a)-(d).
Assertion–Reasonself-inductance of a solenoid $\propto N^2$
Assertion (A): If the number of turns of a solenoid is doubled, its self-inductance becomes four times the original value. Reason (R): The self-inductance of a solenoid is directly proportional to $N$ , the number of turns. Choose the correct option (a)-(d) for the truth of A, R and the explanation.

PreviousResonance & Q-Factor

Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.