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A Copper Wire of Radius 0.1 Mm and Resistance Kω is Connected Across a Power Supply of 20 V. - Physics

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Sum

A copper wire of radius 0.1 mm and resistance kΩ is connected across a power supply of 20 V. (a) How many electrons are transferred per second between the supply and the wire at one end? (b) Write down the current density in the wire.

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Solution

Given:-

Radius of the wire, r = 0.1 mm = 10-4 m

Resistance, R = 1 kΩ = 103 Ω

Voltage across the ends of the wire, V = 20 V

(a) Let q be the charge transferred per second and n be the number of electrons transferred per second.

We know:-

\[i = \frac{V}{R}\]

\[ \Rightarrow i = \frac{20  V}{{10}^3 \Omega}\]

\[ \Rightarrow i = 20 \times  {10}^{- 3}  = 2 \times  {10}^{- 2}   A\]

\[  q = it\]

\[ \Rightarrow q = 2 \times  {10}^{- 2}    \times 1\]

\[ \Rightarrow q = 2 \times  {10}^{- 2}   C\]

Also,

q = ne

\[\Rightarrow n = \frac{q}{e} = \frac{2 \times {10}^{- 2}}{1 . 6 \times {10}^{- 19}}\]

\[ \Rightarrow n = 1 . 25 \times {10}^{17}\]

(b) Current density of a wire,

\[j = \frac{i}{A}\]

\[ \Rightarrow j = \frac{2 \times {10}^{- 2}}{3 . 14 \times {10}^{- 8}}\]

\[ \Rightarrow j = 6 . 37 \times {10}^5 A/ m^2\]

Concept: Current Density
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 10 Electric Current in Conductors
Q 11 | Page 198

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