Answer :

(a) When a bar magnet is pushed towards (or away) from the coil connected to a galvanometer, the pointer in the galvanometer deflects because of the phenomenon of electromagnetic induction.

Factors on which the amount and direction of the deflection depends are

(i) Speed of the magnet

(ii) Polarity of the magnet

Laws describing this phenomenon are

(i) Faraday’s law of electromagnetic induction: The magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit.

(ii) Lenz’s law: The polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.

(b) The flux enclosed by the rod is

for

for

Magnitude of the induced emf is

for

for

Magnitude of the induced current when induced emf is non-zero is

The force required to keep the conductor in motion is

for

for

Variation of flux, emf and force is

OR

The phasor diagram for the series LCR circuit is

The phasor relation for the voltages is

Because V_{C} and V_{L} are always along the same line and in opposite directions, they can be combined into a single phasor (V_{C}+ V_{L}) which has a magnitude

Because V is represented as the hypotenuse of a right triangle whose sides are V_{R} and (V_{C} +V_{L}), the Pythagoras theorem gives

∴

The instantaneous power is

The second term is time dependent. Its average is zero.

∴

At resonance X_{C}=X_{L} and ϕ= 0. So, cosϕ =1 and that is maximum power is dissipated at resonance.

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