## Wednesday, 1 June 2016

### WORKSHEET#8 CURRENT ELECTRICITY DRIFT VELOCITY,MOBILITY,RESITIVITY & NUMBER DENSITY

WORKSHEET#8 CURRENT ELECTRICITY
DRIFT VELOCITY,MOBILITY,RESITIVITY & NUMBER DENSITY

1.A 3000-km long cable consists of seven copper wires, each of diameter 0.73 mm, bundled together and surrounded by an insulating sheath. Calculate the resistance of the cable. Use 3x 10-6ฮฉ. cm for the resistivity of the copper. Ans: 3.1x104 ฮฉ

2.The resistivity of seawater is about 25ฮฉcm . The charge carriers are chiefly Na+ and Cl- ions, and of each there are about 3x1020 / cm3 . If we fill a plastic tube 2 meters long with seawater and connect a 12-volt battery to the electrodes at each end, what is the resulting average drift velocity of the ions, in cm/s? Ans: 2.5x10-5 cm/sec

3. Estimate the average drift speed of conduction electrons in a copper wire of cross section area 2.5 X 10-7m2 carrying a current of 2.7A. Assume the density of conduction electrons to be
9 x 10 28 m3.Ans : 7.5 x10-4 m/s
4. An electron in a hydrogen atom is considered to be revolving around the proton with a velocity ๐2/๐ in circular orbit of radius ๐2/๐๐2. If I is the equivalent current,express it in m,e,n (n=โ2๐)
ANS: I = ๐๐5/2๐๐3
5 .What is the momentum acquired by free electron in a wire of length ‘l’ when current ’I’ flow in the wire? Given m=mass of electron and e = charge on electron.EstablIsh the relation between momentum and mobility ANS:. P=๐๐ผ/๐๐๐ด
6. Two conducting wires X and Y of same diameter but different materials are joined in series across the battery . If the number density of electrons in X is twice that in Y , find the ratio of drift velocity of electrons of the two wires.
ANS:1:2
7.A potential difference V is applied across the ends of copper wire of length l and diameter D. What is the effect on drift velocity if
(i) V is doubled (ii) l is doubled (iii) D is doubled.
Ans:(i) drift velocity doubled (ii) drift velocity halved (iii ) unchanged

8. Estimate the average drift velocity of conduction electron in copper wire of cross sexctional area 1.0 X 10-7m2 carrying the current of 1.5 A. assume the density of conduction of electron 9 X 10 28m-3
A NS:1 mm/sec.

### WORKSHEET #7 CAPACITANCE

WORKSHEET # 7 CAPACITANCE
1.A parallel plate capacitor is charged by a battery, which is then disconnected. A dielectric slab is then inserted in the space between the plates. Explain what changes, if any, occur in the values of:
(i) potential difference between the plates
(ii)Electric field between the plates, and
(iii)The energy stored in the capacitor.
ANS:i)decreases ii)decreases iii)decreases
2. A parallel plate is charged by a battery, When the battery remains connected. A dielectric slab is inserted in the space between the plates. Explain what changes, if any, occur in the the values of:
(i) Electric potential between the plates
(ii) Electric field strength between the plates
(iii ) Capacitance
(iv ) Charge on the the plate
(v ) Energy stored in the capacitor? Justify your answer in each case.
ANS: i)remains same ii)remains sameiii) increases iv) increase v)increases
3. A capacitor has some dielectric between its plates and the capacitor is connected to a DC source. The battery is now disconnected and then the dielectric is removed. State whether the capacitance, the energy stored in it, electric field, charge stored and the voltage will increase, decrease or remains constant.
ANS: Capacitance decreases,Charge remains same,energy stored increases,V increases and E increases
4. A capacitor is connected across a battery.
(i) Why does each plate receive a charge of exactly the same magnitude ?
(ii) Is this true even if the plates are of different sizes?
ANS :i) Due to conservation of charge ii) yes
5. (i) How would you connect two capacitors across a battery, in series or parallel, so that they store greater (a) total charge and (b) total energy?
(ii) What is the dielectric constant of a metal & why?
ANS:i) a)parallel b)parallel ii) infinity
6. A parallel plate capacitor is to be designed with a voltage rating 1KV using a material of dielectric constant 3 and dielectric strength 107 Vm-1 .For safety we would like the field never to exceed, say 10% of the dielectric strength. What minimum area of the plates is required to have a capacitance of 50pF?
ANS: 18.8cm2
7. Two Identical parallel plates ( air) Capacitors C1 and C2 have capacitance C each. The space between their plates is now filled with dielectrics as shown. If the two capacitors still have equal capacitance, obtain the relation between dielectric constant K, K1, K2 .

ANS:K = ½ x(K1+K2)
8.The two plates of a parallel plate capacitor are 4mm apart. A slab of dielectric constant 3 and thickness 3mm is introduced between the plates with its faces parallel to them. The distance between the plates is so adjusted that the capacitance of the capacitor become of its original value . What is the new distance between the plates ?
ANS: 8mm
9. A capacitor of unknown capacitance is connected across a battery of V volt. The charge stored in it Is 360 ฮผC. When potential across the is reduced by 120 V, The charge stored in it becomes 120 ฮผC. Calculate
(i) The potential V and the unknown capacitance C.
(ii) What will be the charge stored in capacitor, if the voltage applied had increased by 120 V.
ANS:i)180V and 2ยตF  ii)600ยตC
10. The plates of a parallel plate capacitor have an area of 90 cm2 each and are separated by 2.5 mm. The capacitor is charged by connecting it to a 400 V supply.
(i) How much electrostatic energy is stored by the capacitor?
(ii) View this energy as stored in the electrostatic field between the plates and obtain the energy per unit volume u. Hence, arrive at the relation between u and the magnitude of electric field E between the plates.
ANS: i) 2.55x 10 - 6 Jii) 2.25 X 10 - 5 m 3  and ½ ฮตoE2
11. Show that the force on each plate of a parallel plate capacitor has a magnitude equal to ½ QE, where Q is the charge on the capacitor and E is the magnitude of electric field between the plates. Explain the origin of factor 1/ 2 .
12. A network of four capacitors each of 12 ฮผF capacitance, if connected to a 500 V supply as shown in figure . Determine
(i) Equivalent capacitance of the network and
(ii) Charge on each capacitor.

ANS:i)16ยตF  ii) 2000ยตC and 6000 ยตC
13.  Five capacitors of capacitance 10ฮผF each are connected with each other, as shown in fig. Calculate the total capacitance between the points A and C.

ANS:10ยตF
14. Two metal plates form a parallel plate capacitor. The distance between the plates is d. A metal sheet of thickness d/2 and of the same area is introduced between the plates. What is the ratio of the capacitance in the two cases?
ANS:2:1
15. Obtain the equivalent capacitance of network in given figure. For a 300V supply, determine the charge and voltage across each capacitor.

ANS: Total capacitance = 66.7 pF and
Potential difference on C 1 = 100 V
Potential difference on C 2 = 50 V
Potential difference on C 3 = 50 V
Potential difference on C 4 = 200 V

### WORKSHEET#6 CAPACITANCE

WORKSHEET # 6 CAPACITANCE
1. A Parallel plate capacitor each with plate area A and separation ‘d’ is charged to a potential    difference V. The battery used to charge it is then disconnected. A dielectric slab of thickness d and dielectric constant 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
(Ansi)charge on the capacitor remains unchanged ii) electric field reduces to 1/K times iii) the capacitance increases)
2. A 2m insulating slab with a large aluminium sheet of area 1m2 on its top is fixed by a man outside his house one evening. Will he get an electric shock, if he touches the metal sheet next morning ?
ANS: Yes
3.Why the capacitance of a parallel plate capacitor increases, on introducing a dielectric medium between the plates?
ANS:As E decreases, V decreases, therefore C increases)
4. A parallel plate capacitor with air between the plates charged. A dielectric is inserted between the plates. What will happen to its electrostatics potential? Give reasons.
ANS:  Q = constant ,C increases , V decrease.
5. The graph shoes the variation of voltage V across the plates of two capacitors A and B versus increase of charge Q stored on them. Which of the capacitors has higher capacitance? Give reason for your answer.
ANS: VA  VB ,therefore CA CB
6.  How does the energy stored in a capacitor change if after disconnecting the battery, the plates of a charged capacitor are moved farther ?
ANS: Increases
7. How does the energy stored in a capacitor change If the plates of a charged capacitor are moved farther, the battery remaining connected?
ANS: Decreases

8. In a parallel plate capacitor with air between the plates, each plate has an area of 6 X 10-3 m2 and the distance between the plates is 3mm. calculate the capacitance of the capacitor. If the capacitor is connected to a 100V supply, what is the charge on each plate of the capacitor?
ANS: 18pF, 1.8 X 10-9 C
9. A slab of material of dielectric constant K has the same area as that of the plates of a parallel plate capacitor but has the thickness d/2, where d is the separation between the plates. Find out the expression for its capacitance when the slab is inserted between the plates of the capacitor.
ANS:C=2 OAK/d(K+1)
10. A parallel plate capacitor with air between the plates has a capacitance of 8 PF. The separation between the plates is now reduced by half and the space between them is filled with a medium of dielectric constant 5 . Calculate the value of capacitance of the capacitor in the second case.
ANS: 80 pF
11.  A very thin plate of metal is placed exactly in the middle of the two plates of a parallel plate capacitor .What will be the effect on the capacitance of the system?
ANS: Capacitance remains unchanged
12. If C1=3 pF and C2=2 pF calculate the equivalent capacitance of the given network between points A and B.

ANS: C = 60/61 PF
13. A parallel plate capacitor of capacitance C is charged to a potential V .It is then connected to another capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor?
ANS: ratio is ½

14.  A technician has only two capacitor. By using them in series or parallel, he is able to obtain the capacitance of 4, 5, 20, 25 ฮผF .What is the capacitance of both capacitor?
ANS: 5ยตF and 20ยตF
15. Net capacitance of three identical capacitors in series is 1 ฮผF. What will be their net capacitance, if connected in parallel? Find the ratio of energy stored in the two configurations, if they are both connected to the same source ?
ANS: ratio is 1/9
16. Three capacitor of capacitance 2 pF,3pF and 4pF and connected in parallel.
(i) What is the total capacitance of the combination?
(ii) Determine the charge on each capacitor, if the combination is connected to a 100V supply
ANS: i)9PF,ii) 200pc,300pc,400pc
17. A 4ฮผF capacitor is charged by a 200V supply. Then, it is disconnected from the supply and is connected to another uncharged 2ฮผF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?
ANS: 2.67 X 10 -2 J