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Question
Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?
Options
R = 20 Ω, L = 1.5 H, C = 35µF.
R = 25 Ω, L = 2.5 H, C = 45µF.
R = 15 Ω, L = 3.5 H, C = 30µF.
R = 25 Ω, L = 1.5 H, C = 45µF.
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Solution
R = 15 Ω, L = 3.5 H, C = 30µF.
Explanation:
Quality factor (Q-factor) of the series resonant circuit:
(i) The characteristic of a series resonant circuit is determined by the quality factor (Q-factor) of the circuit.
(ii) It defines sharpness if i - v curve at resonance when Q-factor is large, the sharpness of resonance curve is more and vice-versa.
(iii) Q-factor is also defined as follows:
Q-factor = `2pi xx "Max energy stored"/"Energy dissipation"`
= `(2pi)/T xx "Max energy stored"/"Mean power dissipated"`
= `"Resonant frequency"/"Bandwidth" = ω_0/(Δω)`
(iv) Q-factor = `V_L/V_R` or `V_C/V_R = (ω_0L)/R` or `1/(ω_0CR)`
⇒ Q-factor = `1/R sqrt(L/C)`
For better tuning of an L-C-R circuit used for communication, quality factor of the circuit must be as high as possible.
We know quality factor should be high for better tuning.
Quality factor (Q) of an L-C-R circuit is `Q = 1/R sqrt(L/C)`
Where R is the resistance, L is the inductance and C is the capacitance of the circuit.
For high Q factor R should be low, L should be high and C should be low.
Important point: Be careful while writing formula for quality factor, this formula we used in this case is only for series L-C-R circuit.
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