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Q.

A horizontal telegraph wire 0.5 km long running east and west in a part of a circuit whose resistance is 2.5 $Ω$ . The wire falls to the ground from a height of 5 m. If g= 10.0 m/s² and B= 2 x 10^-5 weber/m², then the current induced in the circuit is

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a

0.7 amp

b

0.04 amp

c

0.02 amp

d

0.01 amp

answer is C.

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Detailed Solution

$i = \frac{e}{R} = \frac{1}{R} \frac{dΦ}{dt} Here dΦ = B \times A = (2 \times 10^{- 5}) \times (0 \cdot 5 \times 10^{+ 3} \times 5)$
dt = time taken by the wire to fall at ground
$= (2 h / g)^{1 / 2} = (10 / 10)^{1 / 2} = 1 \sec ∴ i = \frac{1}{2 \cdot 5} [\frac{(2 \times 10^{- 5}) \times (0 \cdot 5 \times 10^{3} \times 5)}{1}] = 0 .02 amp$

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