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Physics · 2025 · 5 marks
CBSE 2025 · Region 4 · Set 1 · Q32
(a) (i) State Lenz's law and explain how this law is a consequence of conservation of energy principle. (ii) A square shaped loop of side l/2 is…
(a)(i)
State Lenz's law and explain how this law is a consequence of conservation of energy principle.
(ii)
A square shaped loop of side $\displaystyle \frac{l}{2}$ is initially lying outside a region of uniform magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$ as shown in the figure. The loop is moved towards right with a constant velocity $\displaystyle \overrightarrow{\mathrm{v}}$ till it goes out of the region of magnetic field.
(I)
What will be the directions of induced current when the loop enters the field and when it leaves the field?
(II)
Draw the plots showing the variation of magnetic flux $\displaystyle \phi$ linked with the loop with time t and variation of induced emf E with time t. Mark the relevant values of $\displaystyle \mathrm{E}, \phi$ and t on the graphs.
OR
OR
(b)(i)
Differentiate between peak and rms values of alternating current. How are they related?
(ii)
A current element X is connected across an ac source of emf $\displaystyle \mathrm{V}=\mathrm{V}_{0} \sin 2 \pi \nu \mathrm{t}$. It is found that the voltage leads the current in phase by $\displaystyle \frac{\pi}{2}$ radian. If element X was replaced by element Y, the voltage lags behind the current in phase by $\displaystyle \frac{\pi}{2}$ radian.
(I)
Identify elements X and Y by drawing phasor diagrams.
(II)
Obtain the condition of resonance when both elements X and Y are connected in series to the source and obtain expression for resonant frequency. What is the impedance value in this case?
Marking-scheme solution
(i)
Lenz's law – Polarity of the induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produces it.
When a magnet is moved closer to / away from the loop, the same / opposite pole is developed on the approaching face of the loop. So mechanical work is required to move the magnet, which gets converted into electrical energy — consistent with the law of conservation of energy.
(ii)
(I)
Anticlockwise (when the loop enters)
Clockwise (when the loop leaves)
(i)
Peak value – It is the maximum value of alternating current.
rms value – It is the equivalent dc current that would produce the same average power loss as alternating current.
$\displaystyle I_{\mathrm{rms}}=\frac{I_{0}}{\sqrt{2}}$
(ii)
(I)
X – Inductor (L)
Y – Capacitor (C)
(II)
Impedance of the circuit:
$\displaystyle Z=\left(X_{L}-X_{C}\right)$
At resonance $\displaystyle Z=0$:
$\displaystyle X_{L}=X_{C}$
$\displaystyle \omega L=\frac{1}{\omega C}$
$\displaystyle \omega^{2}=\frac{1}{L C}, \quad \omega=\frac{1}{\sqrt{L C}}$
$\displaystyle \nu=\frac{1}{2 \pi \sqrt{L C}}$
Impedance at resonance $\displaystyle Z=0$
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