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How does drift velocity of electrons in a metallic conductor vary with increase in temperature? Explain.
Concept: Drift of Electrons and the Origin of Resistivity
A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable resistor ‘R’. Plot a graph showing the variation of terminal potential ‘V’ with resistance R. Predict from the graph the condition under which ‘V’ becomes equal to ‘E’.
Concept: Cells, Emf, Internal Resistance
Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.
Concept: Drift of Electrons and the Origin of Resistivity
Obtain the expression for the cyclotron frequency.
Concept: Cyclotron
A deuteron and a proton are accelerated by the cyclotron. Can both be accelerated with the same oscillator frequency? Give reason to justify your answer.
Concept: Cyclotron
Write the expression for the force `vecF` acting on a particle of mass m and charge q moving with velocity `vecV` in a magnetic field `vecB` , Under what conditions will it move in (i) a circular path and (ii) a helical path?
Concept: Force on a Moving Charge in Uniform Magnetic and Electric Fields
Show that the kinetic energy of the particle moving in a magnetic field remains constant.
Concept: Force on a Moving Charge in Uniform Magnetic and Electric Fields
A long straight wire of a circular cross-section of radius ‘a’ carries a steady current ‘I’. The current is uniformly distributed across the cross-section. Apply Ampere’s circuital law to calculate the magnetic field at a point ‘r’ in the region for (i) r < a and (ii) r > a.
Concept: Ampere’s Circuital Law
State the underlying principle of working of a moving coil galvanometer. Write two reasons why a galvanometer can not be used as such to measure current in a given circuit. Name any two factors on which the current sensitivity of a galvanometer depends.
Concept: Moving Coil Galvanometer
Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why?
Concept: Solenoid and the Toroid - the Toroid
Derive the expression for force per unit length between two long straight parallel current carrying conductors. Hence define one ampere.
Concept: Force Between Two Parallel Currents, the Ampere
Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.
Concept: Cyclotron
Predict the polarity of the capacitor in the situation described below :

Concept: The Bar Magnet
Why should the material used for making permanent magnets have high coercivity?
Concept: Permanent Magnet
What is the direction of induced currents in metal rings 1 and 2 when current I in the wire is increasing steadily?

Concept: Lenz’s Law and Conservation of Energy
Show diagrammatically how an alternating emf is generated by a loop of wire rotating in a magnetic field. Write the expression for the instantaneous value of the emf induced in the rotating loop.
Concept: Electromagnetic Induction
Define self inductance. Write its S.I. units.
Concept: Inductance >> Self Inductance
Derive an expression for self inductance of a long solenoid of length l, cross-sectional area A having N number of turns.
Concept: Inductance >> Self Inductance
Why does current in a steady state not flow in a capacitor connected across a battery? However momentary current does flow during charging or discharging of the capacitor. Explain.
Concept: Different Types of AC Circuits: AC Voltage Applied to a Series LCR Circuit
A series LCR circuit is connected to a source having voltage v = vm sin ωt. Derive the expression for the instantaneous current I and its phase relationship to the applied voltage.
Obtain the condition for resonance to occur. Define ‘power factor’. State the conditions under which it is (i) maximum and (ii) minimum.
Concept: Different Types of AC Circuits: AC Voltage Applied to a Series LCR Circuit
