A beam contains 2 . 0 × 10 8 doubly charged positive ions per cubic centimetre, all of which are moving towards the north with a speed of 1 . 0 × 10 5 m s - 1 . (a) What are the magnitude and direction of the current density J → ? (b) Can you calculate the total current i in this ion beam? If not, what additional information is needed?

A doubly charged positive ion has charge, q = + 2 e . Given, number of doubly charged ions per unit volume, n = 2 × 10 8 cm - 3 = 2 × 10 8 × 10 6 m - 3 = 2 × 10 14 m - 3 and drift velocity v d = 1 . 0 × 10 5 m s - 1 (towards north) (a) Magnitude of current density is given by, J = n q v d = 2 × 10 14 × 2 × 1 . 6 × 10 - 19 × 1 . 0 × 10 5 ⇒ J = 6 . 4 A m - 2 . As the charge is positive, so direction of current density is along v d . ∴ J = 6 . 4 A m - 2 towards north. (b) ∵ Current density is given by, J = i A where i is current and A is cross-sectional area. ∴ i cannot be calculated without information of cross-sectional area.

A coil of wire has a resistance of 25 . 00 Ω at 20 ° C and resistance of 25 . 17 Ω at 35 ° C . What is its temperature coefficient of resistance?

Given: Initial resistance of wire R 0 = 25 Ω , final resistance of wire R = 25 . 17 Ω and the change in temperature is ∆ T = 35 ° C - 25 ° C = 10 ° C . Let the temperature coefficient of resistance is α , then the final resistance of the wire can be written as, R = R 0 1 + α ∆ T α = R - R 0 R 0 Δ T α = 25 . 17 - 25 25 × 10 α = 4 . 5 × 10 - 4 ° C - 1 .

A metal wire of diameter 2 mm and of length 300 m has a resistance of 1 . 6424 Ω at 20 ° C and 2 . 415 Ω at 150 ° C . Find the values of α , R 0 and ρ 0 , where the zero subscripts refers to 0 ° C , and ρ 20 ° C ; Identify the metal.

The value of resistance at different temperature will be, R 150 ° C = 2 . 415 Ω = R 0 ( 1 + 150 - 0 α ) . . . 1 R 20 ° C = 1 . 6424 Ω = R 0 ( 1 + 20 - 0 α ) . . . 2 Dividing both equations, R 150 ° C R 20 ° C = R 0 ( 1 + 150 - 0 α ) R 0 ( 1 + 20 - 0 α ) Solving these relations, we get α = 3 . 9 × 10 - 3 ° C - 1 and putting α in equation 1 , we get R 0 = 1 . 5236 Ω Now, the resistance of the wire will be, R 0 = ρ 0 L A ; where L = 300 m and A is area of the cross-section. 1 . 5236 = ρ 0 ( 300 ) π 2 × 10 - 3 2 4 or ρ 0 = 1 . 596 × 10 - 8 Ω m Then, ρ 20 ° C = ρ 0 ( 1 + 20 α ) = 1 . 596 × 10 - 8 1 + 3 . 9 × 10 - 3 ( 20 ) ρ 20 ° C = 1 . 720 × 10 - 8 Ω m . This indicates that the material is copper.

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JEE Advanced

IMPORTANT

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(a) A steady current flows in a metallic conductor of the non-uniform cross-section. State which of the quantities, i.e., current, current density, electric field, and drift velocity remain constant?

(b) A steady current passes through a cylindrical conductor. Is there an electric field inside the conductor?

Important Questions on Electric Current and Circuits

EASY

JEE Advanced

IMPORTANT

PHYSICS for Joint Entrance Examination JEE (Advanced) Electrostatics and Current Electricity>Chapter 5 - Electric Current and Circuits>Concept Application Exercise>Q 2

A potential difference $V$ is applied to copper wire of diameter $d$ and length $L .$ What will be the effect on the electron drift speed, by doubling:

(a) voltage $V$ ,

(b) length $L$ and

HARD

JEE Advanced

IMPORTANT

PHYSICS for Joint Entrance Examination JEE (Advanced) Electrostatics and Current Electricity>Chapter 5 - Electric Current and Circuits>Concept Application Exercise>Q 3

The following table gives the length of three copper rods, their diameters and the potential differences between their ends. Rank the rods according to (a) the magnitude of the electric field within them, (b) the drift speed of electrons through them and (c) the current within them, greatest first.

Rod	Length	Diameter	P.D.
1	$L$	$3 d$	$V$
2	$2 L$	$d$	$2 V$
3	$3 L$	$2 d$	$2 V$

EASY

JEE Advanced

IMPORTANT

PHYSICS for Joint Entrance Examination JEE (Advanced) Electrostatics and Current Electricity>Chapter 5 - Electric Current and Circuits>Concept Application Exercise>Q 4

The $V - I$ graph for a metallic wire at two different temperatures $T_{1}$ and $T_{2}$ is shown in the figure. Which of the two temperatures $T_{1}$ and $T_{2}$ is higher and why?

Question Image

EASY

JEE Advanced

IMPORTANT

PHYSICS for Joint Entrance Examination JEE (Advanced) Electrostatics and Current Electricity>Chapter 5 - Electric Current and Circuits>Concept Application Exercise>Q 5

A beam contains $2.0 \times 10^{8}$ doubly charged positive ions per cubic centimetre, all of which are moving towards the north with a speed of $1.0 \times 10^{5} {m s}^{- 1}$ . (a) What are the magnitude and direction of the current density $\vec{J}$ ?

(b) Can you calculate the total current $i$ in this ion beam? If not, what additional information is needed?

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS for Joint Entrance Examination JEE (Advanced) Electrostatics and Current Electricity>Chapter 5 - Electric Current and Circuits>Concept Application Exercise>Q 6

A typical copper wire might have

2 \times 10^{21}

free electrons in

1 cm

of its length. Suppose that the drift speed of the electrons along the wire is

0.05 cm s^{- 1} .

How many electrons would pass through a given cross-section of the wire each second. How large would a current be flowing in the wire?

EASY

JEE Advanced

IMPORTANT

PHYSICS for Joint Entrance Examination JEE (Advanced) Electrostatics and Current Electricity>Chapter 5 - Electric Current and Circuits>Concept Application Exercise>Q 7

A coil of wire has a resistance of

25.00 Ω

20 ° C

and resistance of

25.17 Ω

35 ° C

. What is its temperature coefficient of resistance?

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS for Joint Entrance Examination JEE (Advanced) Electrostatics and Current Electricity>Chapter 5 - Electric Current and Circuits>Concept Application Exercise>Q 8

A metal wire of diameter

2 mm

and of length

300 m

has a resistance of

1.6424 Ω

20 ° C

and

2.415 Ω

150 ° C

. Find the values of

α, R_{0}

and

ρ_{0},

where the zero subscripts refers to

0 ° C,

and

ρ_{20 ° C};

Identify the metal.

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS for Joint Entrance Examination JEE (Advanced) Electrostatics and Current Electricity>Chapter 5 - Electric Current and Circuits>Concept Application Exercise>Q 9

It is desired to make a

20 Ω

coil of wire, which has a zero thermal coefficient of resistance. To do this, a carbon resistor of resistance

R_{1}

is placed in series with an iron resistor of resistance

R_{2}

. The proportions of iron and carbon are so chosen that

R_{1} + R_{2} = 20 Ω

for all temperatures near

20 ° C

. Find the values of

R_{1}

and

R_{2}

? (

α_{carbon} = - 0.5 \times 10^{- 3 \circ} C^{- 1}, α_{iron} = 5 \times 10^{- 3 \circ} C^{- 1}

Important Questions on Electric Current and Circuits

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