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

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Resonant Frequency Formula

Resonant Frequency Formula

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Q: 17. Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements, and are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified in Exercise 11 (Reference: Chapter 7 Alternating Current Part 3) for this frequency.

Answer:

An inductor (L), a capacitor (C), and a resistor (R) is connected in parallel with each other in a circuit where,

Potential of the voltage source,

Impedance (Z) of the given parallel LCR circuit is given as:

Where,

Angular frequency

At resonance,

Hence, the magnitude of Z is the maximum at. As a result, the total current is minimum.

Rms current flowing through inductor L is given as:

Rms current flowing through capacitor C is given as:

Rms current flowing through resistor R is given as:

Q: 18. A circuit containing a inductor and a capacitor in series is connected to a supply. The resistance of the circuit is negligible.

(A) Obtain the current amplitude and rms values.

(B) Obtain the rms values of potential drops across each element.

(C) What is the average power transferred to the inductor?

(D) What is the average power transferred to the capacitor?

(E) What is the total average power absorbed by the circuit? [‘Average’ implies ‘averaged over one cycle’.]

Answer:

Inductance,

Capacitance,

Supply voltage,

Frequency,

Angular frequency,

Peak voltage,

(A) Maximum current is given as:

The negative sign appears because.

Amplitude of maximum current,

Hence, rms value of current,

(B) Potential difference across the inductor,

Potential difference across the capacitor,

(C) Average power consumed by the inductor is zero as actual voltage leads the current by.

(D) Average power consumed by the capacitor is zero as voltage lags current by.

(E) The total power absorbed (averaged over one cycle) is zero.