Knowledge 1

Electrostatic Potential and Capacitance

1. When two capacitors of capacitance C1 and C2 are connected in series, the net capacitance is 3 µF; whenconnected in parallel its value is 16 µF. Calculate value of C1 and C2.

2. A parallel plate capacitor with air between the plates has a capacitance of 8 pF. The separation betweenthe plates is now reduced by half and the space between them is filled with a medium of dielectricconstant 5. Calculate the value of capacitance in the second case.

3. Two dielectric slabs of dielectric constants K1 and K2 are filled in between the two plates, each of areaA, of the parallel plate capacitor as shown in the Fig. Find the net capacitance of the capacitor.

4. Calculate the capacitance of the capacitor C in the Fig., if the equivalent capacitance of the combinationbetween A and B is 15 µF.

10µF

10µF

C BA

Fig.5. Derive an expression for the electric potential at a point due to a group of n discrete point charges.

6. Calculate the electric potential at the centre of a square, of side 2 m, having charges 100 µC, –50 µC,20 µC and –60 µC at the four corners of this square.

7. Give the dependenc of electrostatic potential due to a small electric dipole at a far off point lying on(i) the axial line, (ii) the equatorial line.

8. Define capacitance of a capacitor. Give its SI unit. Prove the total electrostatic energy stored in a parallel

plate capacitor is12

CV2.

9. Deduce an expression for the capacitance of a parallel plate capacitor with air as the medium betweenthe plates.

10. What is an equipotential surface?

A uniform electric field E

of 300 NC–1 is directed along PQ. A, B and C three points in the field havingx and y coordinates (in metre) as shown in the figure. Calculate potential difference between the points(i) A and B, and (ii) B and C.

A(4, 1)

B(4, 4)

P

xx

y

y

C(–3, 4) E

Fig.

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11. A parallel plate capacitor of plate separation d is charged to a potential difference V. Adielectric slabof thickness d and dielectric constant K is introduced between the plates while the battery remainsconnected to plates.(i) Find the ratio of energy stored in the capacitor after and before the dielectric is introduced. Give the

physical explanation for this change in stored energy.(ii) What happens to the charge on the capacitor?

12. Aparallel plate capacitor with each plate of area A and separation d is charged to a potential differenceV. The battery used to charge it is then disconnected. A dielectric slab of thickness d and dielectricconstant K is now placed between the plates. What change, if any, will take place in

(i) charge on the plates ?(ii) electric field intensity between the plates ?

(iii) capacitance of the capacitor ?Justify your answer in each case.

13. Find theequivalent capacitance between the points A and B of the given combination of capacitors

A B

20µF 10µF

100µF

10µF 5µF

Fig.If a battery of emf 10 V is connected between the points A and B, calculate the total charge in the circuit.

14. Find the total energy stored in the capacitors in the given network of Fig.

1 µFC1

2 µFC4

1 µFC2

C52 µF

2 µFC3

+–6 V

Fig.15. X and Y are two parallel plate capacitors (refer to Fig.) having the same area of plates and same

separation between the plates. X has air between the plates and Y contains a dielectric medium of r =5.(i) Calculate the potential difference between the plates of X and Y.(ii) What is the ratio of electrostatic energy stored in X and Y ?

+ –12 V

X Y

Fig.

Knowledge 3

16. Find (i) eqivalent capacitance and (ii) the total energy in the system of capacitors given in the networkshown in Fig. The charging battery has an emf of 4 V.

12 µF

4µF 3µF

6µF

4 V

+ –

65µF

Fig.17. Name the dielectric whose molecules have (i) non-zero, (ii) zero dipole moment. Define the term

dielectric constant for a medium.18. A conducting slab of thickness ‘t’ is introduced without touching between the plates of a parallel plate

capacitor, separated by a distance ‘d’ (t < d). Derive and expression for the capacitance of the capacitor.19. Draw a labelled diagram of Van-de-Graaff generator. State its principle of working.20. Two parallel plates PQ and RS are kept distance ‘d’ apart. Area of each plate is ‘A’. The space between

them is filled with three dielectric slabs of identical size having dielectric constants K1, K2 and K3,respectively as shown in the Fig. Find the capacitance of the capacitor.

21. (a) Expain how a capacitor store energy on charging. Obtain an expression for the energy thus stored.(b) A battery of 10 V is connected to a capacitor fo 0.1 F. The battery is now removed and the capacitor

is then connected to a second uncharged capacitor of same capacitance. Calculate the total energystored in the system.

22. Explain the effect of introducing a dielectric slab between the plates of a parallel plate capacitor on itscapacitance. Derive an expression for its capacitance with dielectric as the medium between the plates.

23. A dielectric slab of thickness t is kept in between the plates, each of area A, of a parallel plate capacitorseparated by a distance d. Derive an expression for the capacitance of this capacitor for t < d.

24. Find the equivalent capacitance between the point P and Q of the given combination of capacitors,shown in Fig.

P Q

2 µF 6 µF

100µF

4 µF 12 µF

Fig.If a battery of emf 10 V is connected between the points P and Q, calculate the total charge in the circuit.

Moving Charges and Magnetism1. Under waht condition does an electron moving through a magnetic field experience maximum force?2. Under what condition is the force acting on a charge moving through a uniform magmetic field mini-

mum?

4 Knowledge

3. A current is seup in a long copper pipe, Is there a magnetic field (i) inside, (ii) outside the pipe?

4. The force F

experienced by a particle of a charge q moving with velocity v in a magnetic field B

is given by F

= ( )q v B

. Of these, name the pairs of vectors which are always at right angles to eachother.

5. An electron beam projected along + x-axis, experiences a force due to a magnetic field along the + y-axis. What is the direction of the magnetic field ?

6. A charged perticle enters into a uniform magnetic field and experiences an upward force as indicatedin the Fig. What is the charge sign on the particle.

SN

magneticfield

Fig.7. Which one of the following will experience maximum force, when projected with the same velocity ‘v’

perpendicular to the magnetic field:(i) -particle and (ii) -particle?

8. An electron while moving through a region is not deflected. What can be said about this region? Is thereno magnetic field ?

OrAn electron moving through a magnetic field does not experience any force. Under what conditions isthis possible?

9. In the adjoining diagram (Fig.) is shown a circular loop carrying current I. Show the direction of themagnetic field with the help of lines of force.

Fig.10. Which one of the following will have minimum frequency of revolution, when projected with the same

velocity v perpendicular to the magnetic field B: (i) -particle and (ii) -particle.11. An electron and a proton moving parallel to each other in the same direction with equal momenta, enter

into a uniform magnetic field which is at right angles to their velocities. Trace their trajectories in themagnetic field.

12. State two properties of a material used as a suspension wire in a moving coil galvanometer.13. Calculate the magnetic field at the centre of a semi-circular arc of a conductor carrying current.14. An -particle and a proton are accelerated through the same potential difference. Calculate the ratio of

linear momenta acquired by the two particles.15. A steam of electrons travelling with speed v m/s at right angles to a uniform magnetic field ‘B’ is

deflected in a circular path of radius ‘r’. Prove thate vm r B .

16. State the principle of working of a cyclotron. Write two uses of this machine.

Knowledge 5

17. How do you convert a galvanometer into an ammeter ? Why is an ammeter always connected in series?18. Which one of the two, an ammeter or a milliammeter, has a higher resistance and why ?

19. Write the relation of the force F

acting on a charge carrier q moving with a velocity v through amagnetic field B

in vector notation. Using this relation, deduce the conditions under which this force

will be (i) maximum (ii) minimum.20. Two long parallel straight wires X and Y separated by a distance of 5 cm in air carry currents of 10 A

and 5 A, respectively in opposite directions. Calculate the magnitude and direction of the force on a 20cm length of the wire Y.

21. A charged particle, having a charge q, is moving with a speed v along the x-axis. It enters a region ofspace where an electric field E

( ˆEj ) and a magnetic field B

are both present. The particle, on

emerging from this region, is observed to be moving along the x-axis only. Obtain an expression for themagnitude of B

in terms of v and E. Give the direction of B

.

22. A straight wire of lenght L and carrying a current I stays syspended horizontally in mid air in a regionwhere there is a uniform magnetic field B

. The linear mass density of the wire is . Obtain the

magnitude and direction of this magnetic field.23. State Biot-Savart law. Use it to obtain the intensity of magnetic field at a point due to a long, straght

current carrying wire.24. Write the expression for the Biot-Savart’s law for the magnetic field due to a small current carrying

element. Using this expression, valculate the magnetic field intensity at a point on the axis of a circularcurrent carrying conductor.

25. A long solenoid with closely wound turns has n turns per unit of its length. A steady current I flowsthrough this solenoid. Use Ampere’s circuital law to obtain an expression for the magnetic field at a pointon its axis and close to its mid-point.

26. Using Ampere’s circuital law, derive an expression for the magnetic field along the axis of a toroidalsolenoid.

27. A hydrogen ion of mass m and charge q travels with a speed v in a circle of radius r in a magnetic fieldof intensity B. Write the equation in terms of these quantities only, relating the force on the ion to therequired centripetal force. Hence, derive an expression for its time period.

28. Derive an expression for the force acting on a current carrying conductor placed in a uniform magneticfield. Name the rule which gives the direction of the force. Write the condition for which this force willhave (i) maximum (ii) minimum value.

29. Derive an expression for the torque on a rectangular coil of area A, carrying a current I, placea in amagnetic field B. The angle between the direction of B and the vector perpendicular to the plane of thecoil is .

30. A straight wire of length2

m is bent into a circular shape. If the wire wire was to carry a current of

5 A, calculate the magnetic field due to it, before bending, at a point distant 0.01 times the radius of thecircle formed from it. Also calculate the magnetic field at the centre of the circular loop formed for thesame value of current.

31. An infinitely long straight conductor XY is carrying a current of 5 A. An electron is moving with a speedof 105 m/s parallel to the conductor in air from point A to B as shown in Fig. The perpendicular distancebetween the electron and the conductor XY is 20 cm. Calculate the magnitude of the force experiencedby the electron. Write the direction of this force.

6 Knowledge

20 cm

electron

X Y5A

B

Fig.32. 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 ti 7.5 A ? Determine the netresistance of the ammeter. When an ammeter is put in a circuit, does it read slightly less or more thanthe actual current in the original circuit? Justify your answer.

33. Two small identical circular loops, marked (1) and (2), carrying equal currents are placed with thegeometrical axes perpendicular to each other as shown in the Fig. Find the magnitude and direction ofthe net magnetic field at the point O.

(1)

(2)

90ºO

I

I

x

x

Fig.34. Explain the principle and working of a cyclotron with the help of a labelled diagram. A cyclotron’s

oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its ‘dees’ is 60 cm, what is the kinetic energy of the proton beam produced by theaccelerator ? express your answer in units of MeV.(e = 1.6 × 10–19 C, mp = 1.67 × 10–27 kg, 1 MeV = 1.602 × 10–13)

35. Two parallel coaxial circular coils of equal radius ‘R’ and equal number of turns ‘N’, carry equal currents‘I’ in the same direction and are separated by a distance ‘2 R’. Find the magnitude and direction of thenet magnetic field produced at the mid-point of the line joining their centres.

36. With the help of a neat and labelled diagram, explain the underlying principle and woring of a movingcoil galvanometer. What is the function of (i) uniform radial field, (ii) soft iron core in such a device ?

Magnetism and Matter1. Write the SI unit of (i) magnetic pole strenght, (ii) magnetic dipole moment of a bar magnet.2. How does the (i) pole strength, and (ii) magnetic moment of each part of a bar magnet change if it is

cut into two equal pieces along its lenght?3. What should be the orientation of a magnetic dipole in a uniform magnetic field so that its potential

energy is maximum ?4. What is the value of the horizontal component of the earth’s magnetic field at magnetic poles?

Knowledge 7

5. The vertical componnt of earth’s magnetic field at a place if 3 times the horizontal component. Whatis the value of angle of dip at this place?

6. The susceptibility of a magnetic material is –0.085. Identify the magnetic type of the material.7. Steel is preferred for making permanent magnets whereas soft iron is preferred for making electromag-

nets. Explain.8. Why should the material used for making permanent magnets have high coercivity?9. A bar magnet of magnetic moment m is aligned parallel to the direction of a uniform magnetic field B.

What is the work done, to turn the magnet, so as to align its magnetic moment: (i) opposite to the fielddirection and (ii) normal to the field direction?

10. Define the term ‘magnetic dip’ and ‘magnetic declination’ with the help of relevant diagrams.11. A short bar magnet placed with its axis at 30º to a uniform magnetic field of 0.02 T experiences a torque

of 0.060 N m. (i) Calculate magnetic moment of the magnet, adn (ii) find out what orientation of themagnet corresponds to its stable equilibrium in the magnetic field.

12. Write two characteristic properties to distinguish between diamagnetic and paramagnetic materials.13. Why does a paramagnetic substance display greater magnetisation for the same magnetising field when

cooled? How does a diamagnetic substance respond to similar temperature changes?14. Write any three characteristics, a ferromagnetic substance should possess, if it is to be used to make a

permanent magnet. Give one example of such material.15. Where on the earth’s surface is the value of vertical component of the earth’s magnetic field zero? The

horizontal component of the earth’s magnetic field at a ginven place is 0.4 × 10–4 Wb/m2 and angle ofdip is 30º. Calculate the value of (i) vertical component, (ii) the total intensity of the earth’s magneticfield.

16. A short bar magnet placed with its axis inclined at 30º to the external magnetic field of 800 G actinghorizontally experiences torque 0.016 N m. Calculate:(i) the magnetic moment of the magnet.

(ii) the work done by an external force in moving it from most stable to most unstable position.(iii) what is the work done by the force due to the external magnetic field in the process mentioned in

(ii)?17. Explain briefly the elements required to specify the earth’s magnetic field, at a given place. How does

the value of angle of dip vary from the earth’s equator to the north pole?18. Three identical specimens of magnetic materials; nickel, antimony, aluminium are kept in a nonuniform

magnetic field. Draw the modification in the field lines in each case. Justify your answer.

Electromagnetic Iduction1. Write SI unit of magnetic flux. It a scalar or a vector quantity?2. Name the physical quantity whose SI unit is weber. Is it a scalar or a vector quantity?3. Two identical loops, one of copper and another of constanton, are removed from a magnetic field within

the same time interval. In which loop the induced current be greater?4. Give the direction in which the induced current flows in the coil mounted on an insulating stand when

a bar magnet is quickly moved along the axis of the coil from one side to the other as shown in the Fig.

8 Knowledge

S NS N

Fig.5. Define one henry.6. If the self-inductance of an air core inductor increases from 0.01 mH to 10 mH to 10 mH on introducing

an iton core into it, what is the relative permeability of the core used?7. What is induced emf? Write Faraday’s law of electromagnetic induction. Express it mathematically.8. State Lenz’s law. Show that it is a consequence of the law of conservation of energy.9. A cylindrical bar magnet is kept along the axis of a circular coil and near it as shown in the diagram.

Will there be any induced emf at the terminals of the coil, when the magnet is rotated (a) about its ownaxis, and (b) about an axis perpendicular to the length of the magnet?

N S N S

coil coil

(a) (b)

Fig.10. The closed loop PQRS is moving into a uniform magnetic field acting at right angles to the plane of

the paper as shown in the fig. State the direction in which the induced current flows in the loop.11. In the fig. given below, a bar magnet moving towards the right or left induces an emf in the coils (i)

and (ii). Find, giving reason, the directions of the induced currents through the resistors AB and CDwhen the magnet is moving (a) towards the right and (b) towards the left.

A B C D

N S

Fig.12. The fig. shown two identical rectangular loops (1) and (2), placed on a table along with a straight long

current carrying conductor between them.(i) What will be the directions of the induced currents in the loops when they are pulled away from

the conductor with same velocity v ?(ii) Will the emf induced in the two loops be equal ? justify your answer.

Knowledge 9

b

(1) a

x

a

b

x

(2)v v

I

Fig.13. Fig. shown a bar magnet M falling under gravity through an air cored coil C. Plot a graph showing

variation of induced emf (E) with time (t). What does the area enclosed by the E – t curve depict ?

S

NM

V

Fig.14. A bar magnet M is dropped so that it falls vertically through the coil C (Fig.). The graph obtained for

voltage produced across the coil us time is shown in Fig.(a) Explain the shape of the graph.(b) Why is the negative peak longer than the positive peak ?

Magnet

coilCRV

Fig.15. A conducting rod of length l, with one end pivoted, is rotated with a uniform angular speed in a

vertical plane, normal to a uniform magnetic field B. Deduce an expression for the emf induced in thisrod.

16. A rectangular coil of area A having number of turns N is rotated at f revolutions per second in a uniformmagnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in thecoil is 2 f N B A.

17. Define self-inductance. Write down the expression for the self-inductance of a long solenoid of lengthl having N-turns.

18. Write an expression for the energy stored in an inductor when a steady current I is passed through it.Is this energy electric or magnetic?

1 0 Knowledge

19. Name and define the unit used for measuring the coefficient of mutual inductance. State the relation ofthis unit with the units of magnetic flux and electric current.

20. Two circular coils, one of radius r and the other of radius R are placed co-axially with their centrescoinciding. For R >> r, obtain an expression for the mutual inductance of the arrangement.

21. A circular copper disc 10 cm in radius rotates at 20 rad/s about an axis through its centre andperpendicular to the disc. A uniform magnetic field of 0.2 T acts perpendicular to the disc.(i) Calculate the potential difference developed between the axis of the disc and the rim.

(ii) What is the induced current if the resistance of the disc is 2 ?22. A circular coil of radius 8 cm and 20 turns rotates about its vertical diameter with an angular speed of

50 s–1 in a uniform horizontal magnetic field of magnitude 3 × 10–2 T. Find the maximum and averagevalue of the emf inducedin the coil.

23. State and explain Faraday’s law of electromagnetic induction.24. 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 ?

25. A rectangular conductor, LMNO, is placed in a uniform magnetic field B

directed perpendicular to theplane of the conductor (as shown in Fig.). Obtain an expression for the emf induced in the arm MNwhen the arem is moved towards the left with a speed v.Use the above expression to find the emf induced between the ends of an axle of length L of a railwaycarriage travelling on level ground with a speed v. Assume the value of Earth’s magnetic field at theplace to be B and the angle of dip to be .

v

BL M

NO

Fig.26. A metallic square loop ABCD of size of size 15 cm and resistance 1.0 is moved at a uniform velocity

of v m/s in a uniform magnetic field of 2 T, the field lines being normal to the plane of paper. The loopis connected to an electrical network of resistors, each of resistance 2 . Calculate the speed of the loop,for which 2 mA current flows in the loop.

B C

DA

2

2

2

22

Fig.27. A circular coil of N-turn and of radius R is kept normal to a magnetic field given by B = B0 cos t.

Deduce an expression for emf induced in this coil. State the rule which helps to detect the direction ofinduced current.

Knowledge 11

28. Deduce an expresson for the self inductance of a long solenoid of N-turns having a core of relativepermeability r.

29. How is the mutual inductance of a pair of coils affected, when(i) separation between the coils is increased,

(ii) the number of turns of each coil is increased,(iii) a thin iron sheet is placed between the two coils, other factors remaining the same ? Explain your

answer in each case.30. Explain, with the help of diagram, the principle and working of an a.c. generator. Write the expression

for the emf generated in the coil in terms of its speed or rotation.Or

Draw a labelled diagram of an a.c. generator. Explain briefly its principle and working.31. An a.c. generator consists of a coil of 100 turns and cross-sectional area of 3 m2 and is rotating at a

constant angular speed of 60 rad/s in a uniform magnetic field of 0.04 T. The resistance of the coil is500 . Calculate (i) maximum current drawn from the generator, and (ii) maximum power dissipationin the coil.

Alternating Current1. The instantaneous current from an a.c. source is I = 5 sin 314 t ampere. What is the rms value of the

current ?2. When a lamp is connected to an alternating voltage supply, it lights with the same brightness as when

connected to a 12 V d.c. battery. What is the peak value of alternating voltage source?3. The instantaneous emf of an a.c. source is given by E = 300 sin 314 t. What is the rms value of the

emf ?4. What is the phase relationship between current and voltage in (i) an inductor, (ii) a capacitor in an a.c.

circuit?5. Find the vapacitance of the capacitor that would have a reactance of 100 when used with an a.c.

source of frequency5

kHz.

6. In a series LCR circuit, the voltage across an inductor, capacitor and resistor are 20 V, 20 V and 40 V,respectively. What is the phase fifference between the applied voltage and the current in the circuit.

7. Why is there no power consumption in an ideal inductance connected in an a.c. circuit ?8. What is the power dissipation in an a.c. circuit in which voltage and current are given by

V = 300 sin2

t and I = 5 sin t.

9. What is the power dissipated in an a.c. circuit in which voltage and current are given by V = 230 sin

2t and I = = 10 sin t.

10. Prove mathematically that the average value of a.c. over one complete cycle is zero.11. State the underlying principle of an a.c. generator. Write the relationship between the peak value and

rms value of alternating voltage.

1 2 Knowledge

12. An a.c. source E = E0 sin t is applied across an inductor of inductance L. Show mathematically that

the current lags the voltage by a phase angle of2

.

13. Draw the graphs showing the variation of reactance of(a) a capacitor, and(b) an inductor with the frequency of an a.c. circuit.

14. Distinguish between reactance and impedance of an a.c. circuit.15. Write the expression for frequency of an ideal LC circuit. In an actual circuit, why do the oscillations

ultimately die away ?16. (i) Draw the graphs showing variation of inductive reactance and capacitive reactance with frequency

of applied a.c. source.(ii) Can the voltage drop across the inductor or the capacitor in a series LCR circuit be greater than the

applied voltage of the a.c. source? Justify your answer.17. Mention the factors on which the resonant frequency of a series LCR circuit depends. Plot a graph

showing variation of impedance of a series LCR circuit with the frequency of the applied a.c. source.18. Show mathematically that the average power supplied to an ideal capacitor by a source over a complete

cycle of a.c. is zero.19. In India, domestic power supply is at 200 V, 50 Hz, while in USA, it is 110 V, 50 Hz. Give one

advantage and one disadvantage of 220 V supply over 110 V supply.20. A 1 F capacitor is connected to a 220 V, 50 Hz a.c. source. Calculate the rms value of the current

through the circuit. Also find the peak value of voltage across the capacitor.21. A capacitor and a resistor are connected in series with an a.c. source. If the potential difference across

C, R are 120 V, respectively and if the rms current of the circuit is 3 A, calculate the (i) impedance, (ii)power factor of the circuit.

22. A 12 resistance and an inductance of0.05

H are connected in series. Across the ends of this circuit

is connected a 130 V alternating voltage of frequency 50 cps. Calculate the current in the circuit andpotential difference across the inductance.

23. An inductor 200 mH, a capacitor C and a resistor 10 ohm are connected in series with a 100 V,50s–1 a.c. source. If the current and voltage are in phase with each other, calculate the capacitance ofthe capacitor.

24. Calculate the current drawn by the primary of a transformer, which steps down 200 V to 20 V to operatea device of resistance 20 . Assume the efficiency of the transformer to be 80%.

25. Explain with the help of a labelled diagram the underlying principle and working of a step up trans-former. Why cannot such a device be used to step d.c. voltage ?

26. 11 kW of electric power can be transmitted to a distance station at (i) 220 V or (ii) 22,000 V. Whichof the two modes of transmission should be preferred and why? Support your answer with possiblecalculations.

27. When an inductor L and a resisitor R in series are connected across a 12 V, 50 Hz supply, a current of

0.5 A flows in the circuit. The current differs in phase from applied voltage by3

radian. Calculate the

value of R.

Knowledge 13

28. Given below (Fig.) are two electric circuits A and B. Calculate the ratio of power factor of the circuitB to the power factor of circuit A.

~

RX = 3RL

A

~

RX = 3RL

B

X = RC

Fig.29. A 200 V variable frequency a.c. source is connected to a seires combination of L = 5 H, C = 80 F

and R = 40 . Calculate(i) the angular frequency of the source to get maximum current in the circuit.

(ii) the current amplitude at resonance.(iii) the power dissipation in the circuit.

30. In the following circuit (Fig.), calculate, (i) the capacitance ‘C’ of the capacitor, if the power factor ofthe circuit is unity, and (ii) also calculate the Q-factor of the circuit.

~

10

50 s–1

C200 mH

Fig.31. In a series RC circuit, R = 30 , C = 25µF, V = and angular frequency = 10,000 rad/s. Find the current

in the circuit and calculate the voltage across the resistor and the capacitor. Is the algebraic sum of thesevoltages more than the source voltage ? If so, resolve the paradox.

32. A town, situated 20 km away from a power plant generating power at 440 V, requires600 kW of electric power at 220 V. The resistance of the two-wire line carrying power is0.4 per km. The town gets power from the line through a 3000 –220 V step down transformer at asub-station in the town.(i) Find the line power losses in the form of heat.

(ii) How much power must the plant supply, assuming there is negligible power loss due to leakage?33. Figure given belos (fig.) shown, how the reactance of a capacitor varies with frequency.

(i) Use the information on graph to calculate the value of capacity of the capacitor.(ii) An inductor of inductance L has the same reactance as the capacitor at 100 Hz. Find the value of

L.(iii) Using the same axes, draw a graph of reactance against frequency for the inductor given in part

(ii).(iv) If this capacitor and inductor were connected in series to a resistor of 10 , what would be the

impedance of the combination at 300 Hz ?

1 4 Knowledge

14121086420 100 200 300 400

Frequency (Hz)

Rea

ctan

ce(

)

Fig.34. The primary coil of an ideal step up transformer has 100 turns and the transformation ratio is also 100.

The input voltage tna the power are 220 V and 1100 W respectively. Calculate(i) number of turns in the secondary

(ii) the current in the primary(iii) voltage across the secondary(iv) the current in the secondary(v) power in the secondary.