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JIPMER 2004
Exam
JIPMER
Year
2004
Subject
Physics
Chapter
Alternating Current

JIPMER 2004 · Physics · Alternating Current

A transmitting station transmits radiowaves of wavelength 360 m ....

A transmitting station transmits radiowaves of wavelength 360 m . Calculate the inductance of coil required with a condenser of capacity 1.20μF1.20 \mu \mathrm{F} in the resonant circuit to receive them

Options

  1. A3.07×10−8H3.07 \times 10^{-8} \mathrm{H}
  2. B2.07×10−8H2.07 \times 10^{-8} \mathrm{H}
  3. C4.07×10−8H4.07 \times 10^{-8} \mathrm{H}
  4. D60.7×10−8H60.7 \times 10^{-8} \mathrm{H}

Correct answer

A. 3.07×10−8H3.07 \times 10^{-8} \mathrm{H}

Step-by-step solution

The frequency of radiowaves (speed c=3×108 m/s)transmittedc=3 \times 10^8 \mathrm{~m} / \mathrm{s} ) transmittedf=cλ=3×108360=\frac{c}{\lambda}=\frac{3 \times 10^8}{360}=8.3 \times 10^5  Hz\mathrm{~Hz} Frequency of series resonant circuit f=12πLC or L=1(2πf)2C\begin{aligned}f & =\frac{1}{2 \pi \sqrt{L C}} \text{ or } \quad L & =\frac{1}{(2 \pi f)^2 C}\end{aligned}=1(2×3.14×8.3×105)2×1.20×10−6=3.07×10−8H\begin{aligned} & =\frac{1}{\left(2 \times 3.14 \times 8.3 \times 10^5\right)^2 \times 1.20 \times 10^{-6}} \\ & =3.07 \times 10^{-8} \mathrm{H}\end{aligned}$
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