Physics Class 12 NCERT Solutions: Chapter 7 Alternating Current Part 3

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Resonance in LCR circuit is shown.

Resonance in LCR Circuit

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Q: 10. A ratio can tune over the frequency range of a portion of MW broadcast band: If it’s LC circuit has an effective inductance of, what must be the range of its variable capacitor?

[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radio wave.]

Answer:

The range of frequency (v) of a radio is.

Lower tuning frequency,

Upper tuning frequency,

Effective inductance of circuit

Capacitance of variable capacitor for is given as:

Where,

Angular frequency for capacitor

Capacitance of variable capacitor for,

Where,

Angular frequency for capacitor

Hence, the range of the variable capacitor is from.

Q: 11. Figure 7.21 shows a series LCR circuit connected to a variable frequency source.

Q 11 The LCR Circuit Connected to a Variable Frequency

Q 11 the LCR Circuit Connected to a Variable Frequency

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(A) Determine the source frequency which drives the circuit in resonance.

(B) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.

(C) Determine the potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.

Answer:

Inductance of the inductor,

Capacitance of the capacitor,

Resistance of the resistor,

Potential of the variable voltage source,

(A) Resonance angular frequency is given as:

Hence, the circuit will come in resonance for a source frequency of.

(B) Impedance of the circuit is given by the relation,

At resonance,

Amplitude of the current at the resonating frequency is given as:

Where,

Hence, at resonance, the impedance of the circuit is 40 and the amplitude of the current is.

(C) Potential drop across the inductor,

Where,

Current

Potential drop across the capacitor,

Potential drop across the resistor,

Potential drop across the LC combination,

At resonance,

Hence, it is proved that the potential drop across the LC combination is zero at resonating frequency.