Q. 254.0( 2 Votes )

(a) When a bar ma

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 VC and VL are always along the same line and in opposite directions, they can be combined into a single phasor (VC+ VL) which has a magnitude


Because V is represented as the hypotenuse of a right triangle whose sides are VR and (VC +VL), the Pythagoras theorem gives





The instantaneous power is




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




At resonance XC=XL and ϕ= 0. So, cosϕ =1 and that is maximum power is dissipated at resonance.


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