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NCERT Class XII Chapter
Alternating Current
Questions With Solutions

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Question : 10
Total: 26
A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200 μH, what must be the range of its variable capacitor?
Solution:  
For tuning, the natural frequency i.e., the frequency of L-C oscillations should be equal to frequency of radio waves received by the antenna in the form of same frequency current in the L-C circuit. For tuning at 800 kHz, required capacitance
f1 =
1
2π√LC1
 , C1 =
1
4π2Lf12
 =
1
4π2(200×10−6)(800×103)2
 = 197.8 pF
For tuning of 1200 kHz, required capacitance
f2 =
1
2π√LC2
 , C2 =
1
4π2Lf22
 =
1
4π2(200×10−6)(1200×103)2
 = 87.9 pF
So, the variable capacitor should have a frequency range between 87.9 pF to 197.8 pF.
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