Question

A copper wire of radius $0.1\, mm$ and resistance $2\, k \Omega$ is connected across a power supply of $40\, V$. The number of electrons transferred per second between the supply and the wire at one end is

• A. $2.00 \times 10^{16}$
• B. $1.25 \times 10^{17}$
• C. $2.85 \times 10^{17}$
• D. $3.25 \times 10^{16}$

Answer 1

Answer: (B)

Radius of copper wire, $r=0.1\, mm$
$=1 \times 10^{-4} m$
Resistance, $R=2\, k \Omega=2 \times 10^{3} \Omega$
Power supply, $V=40\, V$
Current flowing through the wire,
$I=\frac{V}{R}=\frac{40}{2 \times 10^{3}}=2 \times 10^{-2} A$
$\therefore $ Charge flowing per second
$q=I t=2 \times 10^{-2} \times 1=2 \times 10^{-2} C$
$\therefore $ Number of electrons transferred,
$n=\frac{q}{e}=\frac{2 \times 10^{-2}}{1.6 \times 10^{-19}}$
$=1.25 \times 10^{17}$ electrons