A 5 . 80 m length of 2 . 0 mm diameter wire carries a 750 mA current when 22 . 0 mV is applied to its ends. If the drift speed is 1 . 7 × 10 - 5 ms - 1 , determine (a) The resistance R of the wire (b) The resistivity ρ , and (c) The number n of free electrons per unit volume.

Given: Length of wire, L = 5 . 80 m Radius of wire r = 1 . 0 mm = 1 . 0 × 10 - 3 m Current in the wire i = 750 mA = 750 × 10 - 3 A Drift speed, v d = 1 . 7 × 10 - 5 ms - 1 Potential difference across the ends of wire E = 22 mV = 22 × 10 - 3 V (a) Resistance R of wire can be calculated from Ohm's law. ⇒ R = E i = 22 × 10 - 3 750 × 10 - 3 = 29 . 3 mΩ (b) Resistance, R = ρ L A ⇒ ρ = R A L On substituting the values in above equation, we get ⇒ ρ = 29 . 3 × 10 - 3 π 1 . 0 × 10 - 3 2 5 . 80 = 0 . 015 × 10 - 6 Ωm (c) By using the relation, i = A v d n e . The number density can be calculated as n = i A v d e . On substituting the values we get, n = 750 × 10 - 3 π 1 . 0 × 10 - 3 2 1 . 7 × 10 - 5 1 . 6 × 10 - 19 = 8 . 7 × 10 28 m - 3

At a point high in the Earth's atmosphere, He 2 + ions in a concentration of 2 . 8 × 10 12 m - 3 are moving due north at a speed of 2 . 0 × 10 6 m s - 1 . Also, a 7 . 0 × 10 11 m - 3 concentration of O 2 - ions is moving due south at a speed of 7 . 2 × 10 6 m s - 1 . Determine the magnitude and direction of the net current passing through unit area A m - 2 .

Current density, J is given by, J = v n q , where v , n and e are drift speed, number density and charge of the moving particle. Given: Charge of H e 2 + , q H e = 2 e = 2 × 1 . 6 × 10 - 19 = 3 . 2 × 10 - 19 C Speed of H e 2 + ions, v H e = 2 . 0 × 10 6 m s - 1 Number density of H e 2 + , n H e = 2 . 8 × 10 12 m - 3 Charge of O 2 - , q O 2 = - 1 . 6 × 10 - 19 C Speed of O 2 - , v O 2 = 7 . 2 × 10 6 m s - 1 Number density of O 2 - , n O 2 = 7 . 0 × 10 11 m - 3 Since H e 2 + ions are moving due north and O 2 - ions are moving due south hence the direction of current density due to motion of the two different ions will be in north direction. Conventionally, the direction of current is in the direction of flow of positive charge. J = v H e n H e q H e + v O 2 n O 2 q O 2 On substituting the values in above equation we get J = 2 . 0 × 10 6 2 . 8 × 10 12 3 . 2 × 10 - 19 + 7 . 2 × 10 6 7 . 0 × 10 11 1 . 6 × 10 - 19 J = 2 . 59 A m - 2 , due North.

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A wire of resistance $R$ and of radius $r$ is compressed back to another wire of radius $2 r$ , the new resistance of the wire will be

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Important Questions on Current Electricity

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Gamma Question Bank for Engineering Physics>Chapter 17 - Current Electricity>EXERCISE>Q 10

(a) A group of charges, each with charge

e

, moves with velocity

\vec{v}

. The number of particles per unit volume is

n

. What is the current density of these charges, in magnitude and direction? Make sure that your answer has units of

A m^{- 2}

(b) We want to calculate how long it takes for an electron to get from a car battery to the starter motor after the ignition switch is turned. Assume that the current flowing is $115 A$ , and that the electrons travel through copper wire with cross-sectional area $31.2 {mm}^{2}$ and length $85.5 cm$ . What is the current density in the wire? The number density of the conduction electrons in copper is $8.49 \times 10^{28} m^{- 3}$ . Given this number density and the current density, what is the drift speed of the electrons? How long does it take for an electron starting at the battery to reach the starter motor? Assume no collision.

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Gamma Question Bank for Engineering Physics>Chapter 17 - Current Electricity>EXERCISE>Q 11

At what temperature, the resistance of a copper wire will become three times its value at

0 ° C

? (The average temperature coefficient of resistance for copper

= 4 \times 10^{- 3}

per

{}^{\circ}C

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Gamma Question Bank for Engineering Physics>Chapter 17 - Current Electricity>EXERCISE>Q 12

A $5.80 m$ length of $2.0 mm$ diameter wire carries a $750 mA$ current when $22.0 mV$ is applied to its ends. If the drift speed is $1.7 \times 10^{- 5} {ms}^{- 1}$ , determine

(a) The resistance $R$ of the wire

(b) The resistivity $ρ$ , and

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Gamma Question Bank for Engineering Physics>Chapter 17 - Current Electricity>EXERCISE>Q 13

At a point high in the Earth's atmosphere,

{He}^{2 +}

ions in a concentration of

2.8 \times 10^{12} m^{- 3}

are moving due north at a speed of

2.0 \times 10^{6} m s^{- 1}

. Also, a

7.0 \times 10^{11} m^{- 3}

concentration of

O_{2}^{-}

ions is moving due south at a speed of

7.2 \times 10^{6} m s^{- 1}

. Determine the magnitude and direction of the net current passing through unit area

(A m^{- 2})

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Gamma Question Bank for Engineering Physics>Chapter 17 - Current Electricity>EXERCISE>Q 14

An electrical conductor designed to carry large currents has a circular cross - section $2.50 mm$ in diameter and is $14.0 m$ long. The resistance between its ends is $0 .104 Ω$ .

$(a)$ What is the resistivity of the material?

$(b)$ If the electric field magnitude in the conductor is $1.28 V m^{- 1}$ , what is the total current?

$(c)$ If the material has $8 .5 \times 10^{28}$ free electrons per cubic metre, find the average drift speed under the conditions of part $(b)$ .

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Gamma Question Bank for Engineering Physics>Chapter 17 - Current Electricity>EXERCISE>Q 20

A $1500 W$ radiant heater is constructed to operate at $115 V$ .

(a) What will be the current in the heater?

(b) What is the resistance of the heating coil?

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Gamma Question Bank for Engineering Physics>Chapter 17 - Current Electricity>EXERCISE>Q 21

Given three resistors of resistances $R_{1}, R_{2}$ and $R_{3}$ , how should they be connected to

(a) maximize

(b) minimize the equivalent resistance?

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Gamma Question Bank for Engineering Physics>Chapter 17 - Current Electricity>EXERCISE>Q 22

A wire of resistance

R

is cut into

n

equal parts. These parts are then connected in parallel. The equivalent resistance of the combination will be

A wire of resistance R and of radius r is compressed back to another wire of radius 2 r, the new resistance of the wire will be

Important Questions on Current Electricity

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A wire of resistance $R$ and of radius $r$ is compressed back to another wire of radius $2 r$ , the new resistance of the wire will be