JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Alternating Current

A telegraph line of length 100 km has a capacity of

0.01 μ F / km

and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ____ mH. (if

π = 10

)

Answer: 100

Solution

For minimum impedance in an AC circuit, the inductive and capacitive reactances must be equal:

X_{L} = X_{C}

, which gives

ω L = \frac{1}{ω C}

. Therefore,

L = \frac{1}{ω ^{2} C}

. The total capacitance is

C = 0.01 \times 100 = 1 μ

F =

1 0^{- 6}

F. The angular frequency is

ω = 2 π f = 210 \times 0.5 \times 1 0^{3} = 1 0^{3} 10

rad/s. Thus,

L = \frac{1}{( 1 0 ^{3} 10 ) ^{2} \times 1 0 ^{- 6}} = \frac{1}{1 0 ^{7} \times 1 0 ^{- 6}} = 0.1

H = 100 mH.

JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Integer answer

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