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1. A series battery of 10 lead accumulators each of emf 2 V and internal resistance 0.25 ohm is charged by a 220 V D.C. mains to limit the charging current a resistance of 47.5 ohm is used in series in the charging circuit. What is a) the power supplied by the mains and b) power dissipated as heat? Account for the difference of powers is (a) and (b).
2. A potentiometer wire has a length L and a resistance Ro. It is connected to a battery and
   a resistance combination as shown. Obtain an expression for the potential drop per unit length of this potentiometer wire. What is the maximum emf of a ‘test cell’ for which one can get a ‘balance point’ on this potentiometer wire? What precaution should one take, while connecting this ‘test cell’ , in the circuit?
3. A cell, of emf 4 V and .internal resistance 0.5 Ω, is connected across a load of resistance (i) 7.5 Ω, (ii) 11.5 Ω. Calculate (i) the ratio of the differences in the emf of the cell and the potential drop across the load, and (ii) the ratio of the currents in the two cases.
4. In the figure shown, calculate the total flux of the electrostatic field through the spheres S1 and S2 The wire, AB, shown here, has a linear charge density, λ given by λ = kx where x is the distance measured along the wire, from the end A.
5. A straight wire, of length L, carrying a current I, stays suspended horizontally in mid air in a region where there is a uniform magnetic field B . The linear mass density of the wire is λ. Obtain the magnitude and direction of this magnetic field.
6. Two cells of same emf E, but different internal resistance rl and r2 are connected to an external resistance R as shown. in the figure. The voltmeter V reads zero. Obtain an expression for R in terms of rl and r2. Calculate the voltage across the cell of internal resistance r2. (Assume that the voltmeter V is of infinite resistance).
7. A galvanometer with a coil of resistance 120 ohm shows full scale deflection for a current of 2.5 mA How will you convert the galvanometer into an ammeter of range 0 to 7.5 A ? Determine the net resistance of the ammeter. When an ammeter is put in a circuit, does it read slightly less or more than the actual current in the original circuit? Justify your answer.
8. Figure shows a bar magnet M falling under gravity through an air cored coil C. Plot a graph
   showing the variation of induced e.m.f (E) with time (t). What does the area enclosed by the
   E – t curve depict ?
9. The electron in the hydrogen atom circles around the proton with a speed of 2.18 x 10⁶ m/s in an orbit of radius 5.13 x 10 -11 m. What magnetic field does it produce at the centre?
10. A proton moves with a speed of 7.45 x 10⁵ m/s directly towards a free proton originally at rest. Find the distance of the closest approach for the two protons. (Given: mass of proton = 1.67 x 10^–27 kg and e = 1.6 x 10 ^–19 C)
11. Figure (a), (b) and (c) show three a.c. circuits in which equal currents are flowing. If the frequency of emf be increased, how will the current be affected in these circuits? Give reason for your answer.

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