Question

A current of 30 ampere is flowing through a wire of cross section area 2 mm square

Answer 1

Answer:

A current of 30 ampere is flowing through a wire of cross-sectional area 2mm2. Calculate the drit velocity of electrons. Assuming the temperature of the wire to be 27∘C, also calculate the rms velocity at this temperature.

Explanation:

Answer 2

The complete question is:

A current of 30 ampere is flowing through a wire of cross-sectional area 2mm2. Calculate the drift velocity of electrons. Assuming the temperature of the wire to be 27∘C, also calculate the rms velocity at this temperature. Which velocity is larger ? Given that Boltzman's constant =1.38×10−23JK−1, density of copper 8.9gcm−3, atomic mass of copper =63.

Given:

A current of 30 ampere is flowing through a wire of cross-sectional area 2mm2.  

Given that Boltzman's constant =1.38×10−23JK−1, density of copper 8.9gcm−3, atomic mass of copper =63.

To find:

Calculate the drift velocity of electrons. Assuming the temperature of the wire to be 27∘C, also calculate the rms velocity at this temperature. Which velocity is larger ?  

Solution:

We use the formula,

i = n e A v{d}

where, n = 8.9 × 10-6 / 63

so, we get,

30 = [(8.9 × 10-6)/63] × (1.6 × 10-19) × (2 × 10-6) × v{d}

upon solving, we get,

∴ v{d} = 1.6 × 10^-4 m/s

v{rms} = √3RT/M

v{rms} = √{[3 × 8.3 × (27 + 273)] / 63}

∴ v{rms} = 1.1 × 10^5 m/s

Therefore,  rms velocity is greater than the drift velocity.