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Ques1) A caterpiller of length 4cm crawls in the direction of electron drift along a 5.2mm diameter bare copper wire that carries an uniform current of 12 A. (a) What is the potential difference b/w the two ends of the caterpiller? (b) Is it's tail positive or negative relative to the head? (c) How much time does it takes to crawl 1 cm if it crawlsat the drift speed of the electrons in the wire? (The number of vharge carries per unit volume is 8.49 x 10 28 m-3.)
Ques2) What would happen to the drift velocity of the electrons in a wire and to the current in the wire if the electrons could move freely without the resistance through the wire?
(1)
Area of copper wire : Pi/d*d2 = 2.123x10-5 m2
lenght of catrepillar : L : 0.04 m
Resistivity of copper is: 1.69 x 10-8 ohm-meter
no. density of charge carriers in copper: ρ = 8.49 x 10 28 m-3
(a) volatge V = iR = iρL/A
V = (12*1.69 * 10-8 * 4*10-2) / 2.123x10-5
= 0.382 mV
(b) current i is opposite to electron drift
i runs from Vhig to Vlow
So, the head is at higher potential.
(c) Vd = drift velocity
Δt = Δx / Vd
Vd = J / ne = i / Ane
Δt = Δx .Ane /i
= 10-2 * 2.123x10-5 *8.49*1028 *1.602*10-19 / 12
= 240.5 sec
time it takes to crawl is 240.5 sec
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