Assertion (A): At the instant when magnetic flux is zero, emf induced in the coil is maximum when it is rotating in uniform magnetic field w.r.t. axis in the plane of coil.
Reason (R): emf induced in the coil is equal to rate of change of magnetic flux.
1. Both A & R are true and the (R) is the correct explanation of the (A)
2. Both A & R are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Induced emf is \(E = -d\phi/dt = BA\omega sin(\omega t)\). Magnetic flux is \(\phi = BA cos(\omega t)\). When \(\phi = 0\), \(cos(\omega t) = 0\), which implies \(sin(\omega t) = 1\). Thus, \(E\) is maximum. Both A and R are true, and R correctly explains A.
Assertion (A): Inductance coil are made of copper.
Reason (R): Induced current is more in wire having less resistance.
1. Both A & R are true and the (R) is the correct explanation of the (A)
2. Both A & R are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Inductance coils are made of copper due to its low resistivity, minimizing energy loss. Low resistance allows more induced current for a given EMF (by \(I = V/R\)). Both Assertion (A) and Reason (R) are true, and R explains A.
Assertion (A): Change in magnetic flux w.r.t. time produces an induced emf.
Reason (R): Faraday established induced emf experimentally.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true based on Faraday's Law of electromagnetic induction, \( \epsilon = -\frac{d\Phi_B}{dt} \). Reason (R) is also true as Faraday's experiments confirmed this. (R) correctly explains (A).
Assertion (A): When a coil is rotated in a uniform magnetic field about an axis perpendicular to the field, emf is induced in it which is maximum for the orientation of coil in which magnetic flux through the coil is zero.
Reason (R): In an electric generator, electrical energy is generated by rotating a coil in a magnetic field.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true because \( \epsilon = BA\omega sin(\omega t) \), which is max when \( \Phi_B = BA cos(\omega t) = 0 \). Reason (R) is also true, describing generators. However, (R) is an application and doesn't explain the condition for maximum emf in (A).
Assertion (A): Only a change of magnetic flux with time, will maintain an induced current in the coil.
Reason (R): The presence of a large magnetic flux will maintain an induced current in the coil.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true based on Faraday's Law, which states that induced current is generated only by a change in magnetic flux. Reason (R) is false because a constant magnetic flux, regardless of its magnitude, does not induce a current.
Assertion (A): If a charged particle is released from rest in a time varying magnetic field, it moves in a circle.
Reason (R): In a time varying magnetic field, conservative electric field is induced.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is false; a charged particle released from rest experiences no magnetic force (\(F_B = q(v \times B)\)). While an induced electric field exists, it does not necessarily cause circular motion. Reason (R) is false; a time-varying magnetic field induces a non-conservative electric field.
Assertion (A): At any instant, if the current through an inductor is zero, then the induced emf may not be zero.
Reason (R): An inductor tends to keep the flux constant.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true: The induced EMF is \(emf = -L \frac{dI}{dt}\). Even if \(I=0\) instantaneously, \(frac{dI}{dt}\) can be non-zero (e.g., during oscillation or switching). Reason (R) is true, describing Lenz's law. However, R is not the correct explanation for A, as A focuses on instantaneous values of \(I\) and \(frac{dI}{dt}\).