Assertion (A): The mutual inductance of two coils is doubled if the self-inductance of the primary and secondary coil is doubled.
Reason (R): Mutual inductance \(M \propto \sqrt{L_1 L_2}\).
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
The mutual inductance is given by \(M = k \sqrt{L_1 L_2}\). If \(L_1\) and \(L_2\) are doubled, the new mutual inductance becomes \(M' = k \sqrt{(2L_1)(2L_2)} = 2k \sqrt{L_1 L_2} = 2M\). Thus, (A) is true and (R) correctly explains (A).
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
View Answer
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): A system cannot have mutual inductance without having self inductance.
Reason (R): If mutual inductance of system is zero, its self-inductance must be 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
View Answer
Assertion (A) is true, as mutual inductance \(M\) depends on the self-inductances \(L_1\) and \(L_2\) (\(M \le \sqrt{L_1 L_2}\)). Reason (R) is false; if two coils are perfectly uncoupled (\(k=0\)), their mutual inductance is zero, but their self-inductances \(L_1\) and \(L_2\) can still be non-zero.
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 \(frac{dI}{dt}\).