A current of 10 A exists in a wire of crosssectional area of 5 mm 2 with a drift velocity of 2 × 10-3 ms -1 . The number of free electrons in each cubic meter of the wire is

Question

A current of 10 A exists in a wire of crosssectional area of 5 mm 2 with a drift velocity of 2 × 10-3 ms -1 . The number of free electrons in each cubic meter of the wire is (A) 2 × 106 (B) 625 × 1025 (C) 2 × 1025 (D) 1 × 1023

Tardigrade Admin · Accepted Answer

i =10 A , A =5 mm 2=5 × 10-6 m 2 and v d =2 × 10-3 m / s We know, i = neAvd ∴ 10= n × 1.6 × 10-19 × 5 × 10-6 × 2 × 10-3 ⇒ n =0.625 × 1028=625 × 1025

Q. A current of $10 A$ exists in a wire of crosssectional area of $5 m m^{2}$ with a drift velocity of $2 \times 1 0^{- 3} m s^{- 1} .$ The number of free electrons in each cubic meter of the wire is

$2 \times 1 0^{6}$

$625 \times 1 0^{25}$

$2 \times 1 0^{25}$

$1 \times 1 0^{23}$

$i = 10 A, A = 5 m m^{2} = 5 \times 1 0^{- 6} m^{2}$
and $v_{d} = 2 \times 1 0^{- 3} m / s$
We know, $i = n e A v d$
$∴ 10 = n \times 1.6 \times 1 0^{- 19} \times 5 \times 1 0^{- 6} \times 2 \times 1 0^{- 3}$
$\Rightarrow n = 0.625 \times 1 0^{28} = 625 \times 1 0^{25}$

Q. A current of 10A exists in a wire of crosssectional area of 5mm2 with a drift velocity of 2×10−3ms−1. The number of free electrons in each cubic meter of the wire is

2×106

625×1025

2×1025

1×1023