CBSE CLASS 12 PHYSICS NUMERICALS (SOLVED)
1. A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?
2. What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30º with the direction of a uniform magnetic field of 0.15 T?
3. Two long and parallel straight wires, A and B, carrying currents of 8.0 A and 5.0 A in the same direction, are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.
4. A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically, and the normal to the plane of the coil makes an angle of 30º with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?
5. A short bar magnet placed with its axis at 30° with a uniform external magnetic field of 0.25 T experiences a torque of magnitude 4.5 x 10 ⁻²J. What is the magnitude of the magnetic moment of the bar magnet?
6. A closely wound solenoid of 800 turns and an area of cross-section 2.5 × 10–4 m2 carries a current of 3.0 A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?
The magnetic field of the solenoid has the same pattern as that of a bar magnet. It acts along the axis of the solenoid. Its direction is determined by the sense of flow of current.
7. A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
8. Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V is induced, give an estimate of the self-inductance of the circuit.
9.
a. The peak voltage of an ac supply is 300 V. What is the RMS voltage?
b. The RMS value of current in an ac circuit is 10 A. What is the peak current?
10. A 44 mH inductor is connected to a 220 V, 50 Hz ac supply. Determine the RMS value of the current in the circuit.
11. A 60 µF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the RMS value of the current in the circuit.
12. A series LCR circuit with R = 20 Ω, L = 1.5 H, and C = 35 µF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
When the frequency of the supply equals the natural frequency of the circuit,
13. A 100 µF capacitor in series with a 40 Ω resistance is connected to a 110 V, 60 Hz supply.
(a) What is the maximum current in the circuit?
(b) What is the time lag between the current maximum and the voltage maximum?
14. A power transmission line feeds input power at 2300 V to a step-down transformer, with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V?
15. A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V.
The resistance of the two wirelines carrying power is 0.5 Ω per km. The town gets power from the line through a 4000-220 V step-down transformer at a substation in the town.
(a) Estimate the line power loss in the form of heat.
(b) How much power must the plant supply, assuming there is negligible power loss due to leakage?
(c) Characterise the step-up transformer at the plant.
Line resistance = length of the two wire lines x resistance per unit length
R = 2 x 15 x 0.5 = 15 Ω
The step-up transformer at the plant is 440 V – 7000 V
16 Obtain the binding energy in MeV of a nitrogen nucleus
Atomic mass of nitrogen = 14.00307 u
Mass of a proton = 1.007825 u
Mass of a neutron = 1.008665 u
17. Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be 20cm?
18. (i) The refractive index of glass is 1.5. What is the speed of light in glass? The speed of light in a vacuum is ( 3.0 x 108 m s-1 )
(ii) Is the speed of light in glass independent of the colour of light? If not, which of the two colours, red and violet, travels slower in a glass prism?
19. A beam of light converges at a point P. Now, a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm and (b) a concave lens of focal length 16cm?
The image is formed 7.5cm away from the lens towards its right.
The image is formed 48cm away from the lens towards its right.
20. A battery of EMF 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?
21. At room temperature (27.0 °C) the resistance of a heating element is 100 Ω. What is the temperature of the element if the resistance is found to be 117 Ω, given that the temperature coefficient of the material of the resistor is 1.70 × 10–4 °C–1.
22. A negligibly small current is passed through a wire of length 15 m and uniform cross-section 6.0 × 10–7 m2, and its resistance is measured to be 5.0 Ω. What is the resistivity of the material at the temperature of the experiment?
23. Determine the current in each branch of the network shown in the figure:
25. Three capacitors of capacitances 2 pF, 3pF and 4pF are connected in parallel.
(b) Find the charge on each capacitor if the combination is connected to a 100 V supply.
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