11. A copper wire of radius 0.1 mm and resistance 1 ks is
connected across a power supply of 20 V. Write down the current
density in the wire.
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Sol.
r = 0.1 mm = 10^-4
R = 1 KΩ = 10^3 Ω,
V = 20 V
a) No.of electrons transferred
i = V/R = 20/10^3 = 20 * 10^-3 = 2 * 10^-2 A
q = i t = 2 * 10^-2 * 1 = 2 * 10^-2 C.
No. of electron transferred = 2 * 10^-2/1.6 * 10^-19 = 2 * 10^-17/1.6 = 1.25 * 10^17.
b)Current density of wire = i/A = 2 * 10^-2/π * 10^10^-8
= 2/3.14 * 10^+6 0.6369 * 10^+6
= 6.37 * 10^5 A/m^2.
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