PHYSICS WORKSHEET CLASS : XII Topic: Alternating current 1. What is mean by root mean square value of alternating current? 2. Distinguish between the terms effective value and peak value of an alternating current. 3. Show that in an a.c circuit containing pure resistor, the current in phase with the voltage. 4. Show that in an a.c circuit containing pure inductor, the voltage is ahead of current by π/2 in phase. 5. An a.c voltage E = E o sin ωt is applied across a pure capacitor of capacitance C. Show that the current flowing through it leads the applied voltage by a phase angle of π/2. 6. Show graphically the variation of inductive reactance with frequency of the applied alternating voltage. 7. Show graphically the variation of capacitive reactance with frequency of the applied alternating voltage. 8. Prove that an ideal inductor does not dissipate power in an a.c circuit. 9. Prove that an ideal capacitor does not dissipate power in an a.c circuit 10. Derive an expression for the impedance of a series LCR circuit connected to an AC supply of variable frequency by using phasor diagram. 11. A series LCR circuit is connected to an ac source having voltage V= V o sinωt Derive the expression for the instantaneous current and its phase relationship to the applied voltage. 12. Obtain the condition for resonance in LCR circuit. Define power factor. State the conditions under which it is (i)maximum and (ii) minimum. 13. Explain how the phenomenon of resonance in the circuit can be used in tuning mechanism of a radio or a TV set. Page 1 of 4
14. Derive an expression for the average power consumed in a series LCR circuit connected to a.c. source in which the phase difference between the voltage and the current in the circuit is φ. 15. Define the quality factor in an a.c circuit. Why should the quality factor have high value in receiving circuits? Name the factors on which it depends? 16. What do you understand by sharpness of resonance in series LCR circuit? Derive an expression for Q- factor of the circuit. 17. State the principle on which AC generator works. Draw a labelled diagram and explain its working. 18. A coil of an a.c generator having N turns, each of area A, is rotated with a constant angular velocity ω. Deduce the expression for the alternating e.m.f generated in the coil. 19. Derive the expression for frequency of an ideal LC circuit. In actual circuit, why do the oscillation ultimately die away? Level 2 20. An electric lamp connected in series with a capacitor and an ac source, is glowing with of certain brightness. How does the brightness of the lamp change on reducing the (i) capacitance (ii) frequency? 21. In the given circuit, the potential difference across the inductor L and resistor R are 200 V and 150 V respectively and the rms value of current is 5 A. Calculate (i) the impedance of the circuit and (ii) the phase angle between the voltage and the current. Page 2 of 4
22. Draw the graphs showing the variations of (i) inductive reactance, and (ii) capacitive reactance, with frequency of the applied voltages in a.c circuit. How do the values of (i) inductive and (ii) capacitive reactance change, when the frequency of applied voltage is tripled? 23. 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. 24. The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are 220 V and 1100 W respectively. Calculate (i) The number of turns in the secondary coil (ii) The current in the primary coil (iii) The voltage across the secondary coil (iv) The current in the secondary coil (v) The power in the secondary coil. 25. A device X is connected to an a.c source. The variation of voltage, current and power in one complete cycle is shown in the figure. (a) Which curve shows power consumption over a full cycle? (b) What is the average power consumption over a cycle? (c) Idetify the device X. Level 3 26. An alternating voltage given by V= 140 sin 314 t is connected across a pure resistor of 50 Ω. Find (i) the frequency of the source Page 3 of 4
(ii) The rms current through the resistor. 27. An inductor 200 mh, capacitor 500µF, resistor 10 Ω are connected in series with a 100 V frequency ac source. Calculate the (i) Frequency at which the power factor of circuit is unity (ii) Current amplitude at this frequency (iii) Q-factor 28. Calculate the current drawn by the primary coil of a transformer which steps down 200 V to 20 V to operate a device of resistance 20 Ω. Assume the efficiency of the transformer to be 80 %. 29. Determine the current quality factor at resonance for a series LCR circuit with L=1.00 mh, 1.00 nf and R= 100 Ω connected to an ac source having peak voltage of 100 V. Page 4 of 4
PHYSICS WORKSHEET CLASS : XII Chapter 6 Topic: Electromagnetic Induction LEVEL 1 1. State Faraday s law of electromagnetic induction. (notes.pg.no.3) 2. State Lenz s law. Two identical loops, one of copper and the other of aluminium are rotated with the same speed, in a uniform magnetic field acting normal to the plane of the loops. State with reason, for which of the coils (i) induced emf, (ii) induced current, will be more. (notes.pg.no.3) Ans. (i) Induced emf will be same because rate change of flux through each loop is same. (ii) Resistivity of copper is lesser than that of aluminium. So induced current in copper is more. 3. A conducting rod of length Ɩ is moved in a magnetic field of magnitude B with velocity V such that the arrangement is mutually perpendicular. Prove that the emf induced in the rod is ε = BƖv. (notes.pg.no.5) 4. What are eddy currents? How are these produced? In what sense are eddy currents considered undesirable in a transformer and how are these reduced in such a device? (notes.pg.no.7,8) Write applications of eddy currents. (notes.pg.no.9) 5. Write SI units of self-inductance and mutual inductance. An. SI units of both are Henry(H) 6. Define self-inductance of a coil. Show that magnetic energy required to build up the current I in a coil of self inductance L, is given by ½ LI 2. (notes.pg.no.9,11) 7. Deduce an expression for the self inductance of a long solenoid of N turns, having a core of relative permeability µ r. (notes.pg.no.10) 8. Define mutual inductance between two long coaxial solenoids. Find out the expression for the mutual inductance of inner solenoid of length Ɩ having the radius r 1 and number of turns n 1 per unit length due to the second outer solenoid of same length and n 2 number of turns per unit length. (notes.pg.no.11,12) 9. How is the mutual inductance of a pair of coils affected when: Page 1 of 4
(i) Separation between the coils is increased? (ii) The number of turns of each coils is increased? (iii) A thin iron sheet is placed between the two coils, other factors remaining the same?. Explain your answer in each case. Ans. (i) When distance between the coils increases, leakage of flux increases. So mutual inductance decrases. (ii) According to eqn.,when number of turns increases, mutual inductance increases. (iii) When thin sheet is placed between coils, mutual inductance decreases due to opposite eddy current set-up in the sheet. As rate of change of magnetic flux in the coil decreases, induced emf also decreases. Hence mutual inductance decreases. 10. State the principle on which AC generator works. Draw a labelled diagram and explain its working. (notes pg.no.13,14) 11. A coil of an a.c generator having N turns, each of area A, is rotated with a constant angular velocity ω. Deduce the expression for the alternating e.m.f generated in the coil. (notes.pg.no.14) 12. A rectangular coil of area A, having number of turns N is rotated at f revolutions per second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is 2πf NBA. (notes.pg.no.14) LEVEL 2 13. The given graph shows a plot of magnetic flux and the electric current flowing through two inductors P and Q. Which of the two inductors has smaller value of self inductance? 14. Two circular coils, one of radius r and the other of radius R are placed coaxially with their centers coinciding. For R>> r, obtain an expression for the mutual inductance of the arrangement. Page 2 of 4
15. The current flowing through an inductor of self inductance L is continuously increasing. Plot a graph showing the variation of (a) Magnetic flux versus the current (b) Induced emf versus di/dt (c) Magnetic potential energy stored versus the current. 16. The currents flowing in the two coils of self inductance L 1 =16 mh and L 2 = 12 mh are increasing at the same rate.if the power supplied to the coils are equal, find the ratio of (i) induced voltages, (ii) the currents, (iii) the energies stored in the two coils at a given instant. LEVEL 3 17. Predict the direction of induced current in a metal ring when the ring is moved towards a straight conductor with constant speed v. The conductor is carrying current I in the direction shown in the figure. 18. The current flowing in a wire in the direction from B to A is decreasing. Find out the direction of the induced current in the metallic loop kept above the wire as shown. Page 3 of 4
19. Give the direction in which induced current flows in the wire loop, when the magnet moves towards the loop as shown. 20. Predict the directions of induced currents in metal rings 1 and 2 lying in the same plane where current I in the wire is increasing steadily. 21. The loop abc is moved completely inside the magnetic field which is normal to the loop, to a new position a b c. What is the direction of the current induced in the loop? ******************************************* Page 4 of 4