Q15 of 805 Page 1

Two material bars A and B of equal area of cross-section, are connected in series to a DC supply. A is made of usual resistance wire and B of an n-type semiconductor.

(a) In which bar is drift speed of free electrons greater?


(b) If the same constant current continues to flow for a long time, how will the voltage drop across A and B be affected?


Justify each answer.

a) As we know that the drift velocity depends on the current as,



Where n is the no. of charge carriers per unit volume, e is the charge of an electron, I is the current flowing and A is the area of cross section of the resistance.


As we know that,


nmetals>nsemiconductors


so, for the same value of current and same area of cross-section the drift velocity of electrons in metal resistance is smaller than in the n-type semiconductor.


b) If the same constant current continues to flow for a long time, the voltage drop across A will increase as the resistance of metal increases with increase in temperature but will decrease in B as the resistance of a semiconductor decreases with increase in temperature.


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(a) An electric dipole is kept first to the left and then to the right of a negatively charged infinite plane sheet having a uniform surface charge density. The arrows P1 and P2 show the directions of its electric dipole moment in the two cases.


Identify for each case, whether the dipole is in stable or unstable equilibrium. Justify each answer.


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Will the dipole be in equilibrium at these two positions? Justify your answer.

16

Derive an expression for the velocity vC of positive ions passing undeflected through a region where crossed and uniform electric field E and magnetic field B are simultaneously present.

Draw and justify the trajectory of identical positive ions whose velocity has a magnitude less than vC.


OR


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Find magnitude and direction of electric field required so that the particle goes undeflected.

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A sinusoidal voltage of peak value 10 V is applied to a series LCR circuit in which resistance, capacitance and inductance have values of 10 Ω, 1μF and 1H respectively. Find (i) the peak voltage across the inductor at resonance (ii) quality factor of the circuit.