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): A transformer cannot work on D.C. supply.
Reason (R): D.C. changes neither in magnitude nor in direction.
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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Transformers rely on mutual induction, which requires a changing magnetic flux. DC current, being constant (R), produces a steady flux, thus no induced EMF. Both A and R are true, and R correctly explains A.
Assertion (A): Magnetic flux is a vector quantity.
Reason (R): Value of magnetic flux cannot be negative.
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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Magnetic flux \(\phi = \vec{B} \cdot \vec{A}\) is a scalar quantity (A is false). Also, \(\phi = BA cos\theta\) can be negative when \(cos\theta\) is negative, indicating direction relative to area normal (R is false). Both are false.
Assertion (A): An emf is induced in a closed loop where magnetic flux is varied. The induced electric field is not a conservative field.
Reason (R): For induced electric field, the line integral \( \oint \vec{E} \cdot d\vec{l} \) around a closed path is non-zero.
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 varying magnetic flux induces a non-conservative electric field. Reason (R) is true; for a non-conservative field, \( \oint \vec{E} \cdot d\vec{l} \neq 0 \). (R) correctly explains why the induced electric field is non-conservative.
Assertion (A): It is more difficult to push a magnet into a coil with more loops.
Reason (R): This is because emf induced in each current loop resists the motion of the magnet.
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. More loops increase induced emf and current, strengthening the opposing magnetic field. Reason (R) is true due to Lenz's law, where induced effects oppose the cause. (R) provides the direct explanation for (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): If we use a battery across the primary of a step up transformer, no voltage is obtained across secondary.
Reason (R): Battery gives a steady current.
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. Transformers require a changing magnetic flux to induce voltage. Reason (R) is true; a battery provides DC current. This steady current causes constant flux, hence no induced emf in the secondary. (R) correctly 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): 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
View Answer
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.