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Alternating Current — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsAlternating Current3 Marks
Question

In a series LCR circuit connected to an ac source of variable frequency and voltage v vm= sin, draw a plot showing the variation of current (I) with angular frequency ($\omega$) for two different values of resistance R1 and R2(R1 > R2 ). Write the condition under which the phenomenon of resonance occurs. For which value of the resistance out of the two curves, a sharper resonance is produced? Define Q-factor of the circuit and give its significance.

✓

Answer


At certain frequency $\omega$, the flow of current through the series combination
$\text{I}_{m} = \frac{\text{v}_{m}}{\sqrt{\text{R}^{2} + (\text{x}_{L} - \text{x}_{C}^{2}})}$
Where XL = $\omega_{L}$
and
$\text{X}_{C} = \frac{1}{\omega\text{C}}.$
Condition of resonance – If systemis (LCR) of natural frequency $\omega_{0}$ is driven by an energy source at a frequency $\omega$, the amplitude of the current flow increases, however the amplitude of the current rises to its maximum value, if frequency of the energy source becomes exactly equal to the natural frequency.
For resistance R2 < R1, series LCR shows a sharp resonance.
Q-factor – The ratio of reactance (either inductive or capacitive) at natural frequency to the resistance of the current is called Q - factor
$\text{Q} = \frac{\text{X}_{L}}{\text{R}} = \frac{\omega_{0}\text{L}}{\text{R}}$

Significance:
  1. If resistance R is low or inductance L is large then Q – factor is large and the circuit is more selective.
  2. If resonance is less sharp, tunning of the circuit will not be good.

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