Question 123: AC fundamentals

Question

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 $$\mu$$F is used in the resonant circuit. The self inductance of coil necessary for resonance is __________ $$	imes$$ 10$$-$$8 H.

Accepted Answer

$$\lambda$$ = 960 m
C = 2.56 $$\mu$$F = 2.56 $$	imes$$ 10
$$-$$6
F
c = 3 $$	imes$$ 10
8
m/s
L = ?
Now at resonance, $${\omega _0} = {1 \over {\sqrt {LC} }}$$
[Resonant frequency]
$$2\pi {f_0} = {1 \over {\sqrt {LC} }}$$
On substituting $${f_0} = {c \over \lambda }$$, we have $$2\pi {c \over \lambda } = {1 \over {\sqrt {LC} }}$$
Squaring both sides : $$4{\pi ^2}{{{c^2}} \over {{\lambda ^2}}} = {1 \over {LC}}$$
$$ = {{4 	imes 10 	imes {{(3 	imes {{10}^8})}^2}} \over {{{(960)}^2}}} = {1 \over {L 	imes 2.56 	imes {{10}^{ - 6}}}}$$
$$ \Rightarrow {1 \over L} = {{4 	imes 10 	imes 9 	imes {{10}^{16}} 	imes 2.56 	imes {{10}^{ - 6}}} \over {960 	imes 960}}$$
$$ \Rightarrow L = 10 	imes {10^{ - 8}}$$ H

AC fundamentals

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 $\muF is used in the resonant circuit. The self inductance of coil necessary for resonance is __________ \times 10-$8 H.

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