Q: A wire carries a current of 2.0 A. What is the charge that has flowed through its cross-section in 1.0 s ? How many electrons does this correspond to?

Solution ∵i=tq∴q=it=(2.0 A)(1.0 s)=2.0Cq=nen=eq=1.6×10−192.0=1.25×1019

Q: The current in a wire varies with time according to the relationi=(3.0 A)+(2.0 A/s)t(a) How many coulombs of charge pass a cross-section of the wire in the time interval between t=0 and t=4.0 s ?(b) What constant current would transport the same charge in the same time interval?

(a) i=dtdq∫0qdq=∫04idtq=∫04(3+2t)dt=[3t+t2]04=[12+16]=28C(b) i=tq=428=7 A

Q: How many electrons per second pass through a section of wire carrying a current of 0.7 A ?

∵i=tq=tne∴n=eit=1.6×10−19(0.7)(1)=4.375×1018

Q: A current of 7.5 A is maintained in wire for 45 s. In this time,(a) how much charge and(b) how many electrons flow through the wire?

(a) ∵q=it=(7.5)(45)=337.5C(b) n=eq=1.6×10−19337.5=2.1×1021

Q: In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5.3×10−11 m with a speed of 2.2×106 m/s. Determine its frequency f and the current I in the orbit.

f=2πrv=(2π)(5.3×10−11)2.2×106=6.6×1015 HzI=qf=(1.6×10−19)(6.6×1015)=1.06×10−3 A=1.06 mA

Q: The current through a wire depends on time as, i=(10+4t)Here, i is in ampere and t in seconds. Find the charge crossed through a section in time interval between t=0 to t=10 s.

Δq=∫010idt=∫010(10+4t)dt=300C

Question 1

In a given time of 10 s,40 electrons pass from right to left. In the same interval of time 40 protons also pass from left to right. Is the average current zero? If not, then find the value of average current.

Accepted Answer

No, the average current is not zero. Direction of current is the direction of motion of positive charge or in the opposite direction of motion of negative charge. So, both currents are from left to right and both currents will be added.∴Iav​=Ielectron​+Iproton​=t1​q1​​+t2​q2​​=1040e​+1040e​(q=ne)=8e=8×1.6×10−19 A=1.28×10−18 A

Question 2

A constant current of 4 A passes through a wire for 8 s. Find total charge flowing through that wire in the given time interval.

Accepted Answer

Since, i= constant∴Δq=i×Δt=4×8=32C

Question 3

A wire carries a current of 2.0 A. What is the charge that has flowed through its cross-section in 1.0 s ? How many electrons does this correspond to?

Accepted Answer

Solution ∵i=tq​∴q=it=(2.0 A)(1.0 s)=2.0Cq=nen=eq​=1.6×10−192.0​=1.25×1019

Question 4

The current in a wire varies with time according to the relationi=(3.0 A)+(2.0 A/s)t(a) How many coulombs of charge pass a cross-section of the wire in the time interval between t=0 and t=4.0 s ?(b) What constant current would transport the same charge in the same time interval?

Accepted Answer

(a) i=dtdq​∫0q​dq=∫04​idtq=∫04​(3+2t)dt=[3t+t2]04​=[12+16]=28C(b) i=tq​=428​=7 A

Question 5

Current passing through a wire decreases linearly from 10 A to 0 in 4 s. Find total charge flowing through the wire in the given time interval.

Accepted Answer

Current versus time graph is as shown in figure. Area under this graph will give us net charge flow.Hence,Δq=Area=21​×base×height=21​×4×10=20C

Question 6

How many electrons per second pass through a section of wire carrying a current of 0.7 A ?

Accepted Answer

∵i=tq​=tne​∴n=eit​=1.6×10−19(0.7)(1)​=4.375×1018

Question 7

A current of 3.6 A flows through an automobile headlight. How many coulombs of charge flow through the headlight in 3.0 h?

Accepted Answer

∵q=it=(3.6)(3×60×60)=38880C

Question 8

A current of 7.5 A is maintained in wire for 45 s. In this time,(a) how much charge and(b) how many electrons flow through the wire?

Accepted Answer

(a) ∵q=it=(7.5)(45)=337.5C(b) n=eq​=1.6×10−19337.5​=2.1×1021

Question 9

In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5.3×10−11 m with a speed of 2.2×106 m/s. Determine its frequency f and the current I in the orbit.

Accepted Answer

f=2πrv​=(2π)(5.3×10−11)2.2×106​=6.6×1015 HzI=qf=(1.6×10−19)(6.6×1015)=1.06×10−3 A=1.06 mA

Question 10

The current through a wire depends on time as, i=(10+4t)Here, i is in ampere and t in seconds. Find the charge crossed through a section in time interval between t=0 to t=10 s.

Accepted Answer

Δq=∫010​idt=∫010​(10+4t)dt=300C

Question 11

In an electrolyte, the positive ions move from left to right and the negative ions from right to left. Is there a net current? If yes, in what direction?

Accepted Answer

Current due to both is from left to right. So, the two currents are additive.

Question 12

Electric field inside a conductor is always zero. Is this statement true or false?

Accepted Answer

False. Under electrostatic conditions when there is no charge flow (or no current) in the conductor, electric field is zero. If current is non-zero, then electric field is also non-zero. Because the drift motion (of free electrons) which produces a net current starts only due to electric force on them.

Question 13

All points of a conductor are always at same potential. Is this statement true or false?

Accepted Answer

False. Only under electrostatic conditions (when i=0 ) all points of a conductor are at same potential.

Question 14

An electron beam has an aperture of 1.0 mm2. A total of 6.0×1016 electrons go through any perpendicular cross-section per second. Find (a) the current and (b) the current density in the beam.

Accepted Answer

(a) The current is given byi=tq​=tne​Substituting the values we have,i=1(6.0×1016)(1.6×10−19)​=9.6×10−3 A(b) The current density isj=Ai​=10−69.6×10−3​=9.6×103 A/m2

Question 15

Calculate the drift speed of the electrons when 1 A of current exists in a copper wire of cross-section 2 mm2. The number of free electrons in 1 cm3 of copper is 8.5×1022.

Accepted Answer

n= free electron density,=8.5×1022 per cm3=(8.5×1022)(106) per m3From i=neAvd​, we getvd​=neAi​Substituting the values in SI units we have,vd​=(8.5×1028)(1.6×10−19)(2×10−6)1​=3.6×10−5 m/s

Question 16

When a wire carries a current of 1.20 A, the drift velocity is 1.20×10−4 m/s. What is the drift velocity when the current is 6.00 A ?

Accepted Answer

i=neAvd​i.e. vd​∝iWhen current has increased from i=1.2 A to i=6.0 A, i.e five times, then drift velocity will also increase to five times.

Question 17

Find the velocity of charge leading to 1 A current which flows in a copper conductor of cross-section 1 cm2 and length 10 km. Free electron density of copper is 8.5×1028/m3. How long will it take the electric charge to travel from one end of the conductor to the other?

Accepted Answer

From i=neAvd​We have vd​=neAi​or vd​=8.5×1028×1.6×10−19×10−41​=0.735×10−6 m/s=0.735μm/st=vd​l​=0.735×10−610×103​ s=0.735×10−6×60×60×24×36510×103​yr=431.4yr

Question 18

Two copper wires of the same length have got different diameters,(a) which wire has greater resistance?(b) greater specific resistance?

Accepted Answer

Solution (a) For a given wire, R=ρAl​, i.e. R∝A1​So, the thinner wire will have greater resistance.(b) Specific resistance ( ρ ) is a material property. It does not depend on l or A. So, both the wires will have same specific resistance.

Question 19

A wire has a resistance R. What will be its resistance if it is stretched to double its length?

Accepted Answer

Solution Let V be the volume of wire, thenV=Al∴A=lV​Substituting this in R=ρAl​, we have R=ρVl2​So, for given volume and material (i.e. V and ρ are constants)R∝l2When l is doubled, resistance will become four times, or the new resistance will be 4R.

Question 20

The dimensions of a conductor of specific resistance ρ are shown below. Find the resistance of the conductor across AB,CD and EF.

Accepted Answer

R=ρAl​Resistance across AB,CD and EF in tabular form is shown below.

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Solutions for Electricity and Magnetism by DC Pandey

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