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Q.

A radio tuner has a frequency range from 500 kHz to 5 MHz. If its LC circuit has an effective inductance of 200 $μ$ H, what is the range of its variable capacitor? $(Take π^{2} = 10) .$

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a

2.5 pF to 250 pF

b

5.0 pF to 500 pF

c

7.5 pF to 750 pF

d

10 pF to 1000 pF

answer is B.

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Detailed Solution

$n = \frac{1}{2 π \sqrt{LC}} \Rightarrow C = \frac{1}{{(2 πn)}^{2} L} \Rightarrow C_{1} = \frac{1}{{(2 \times 3.14 \times 500000)}^{2} \times 200 \times 10^{- 6}} \Rightarrow C_{1} = 500 pf \Rightarrow C_{2} = \frac{1}{{(2 \times 3.14 \times 5000000)}^{2} \times 200 \times 10^{- 6}} \Rightarrow C_{2} = 5 pf$

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A radio tuner has a frequency range from 500 kHz to 5 MHz. If its LC circuit has an effective inductance of 200 μH, what is the range of its variable capacitor? (Take π2=10.