Ncert Exercises & Solutions

Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?
1. $R = 20~\Omega,~L= 1.5~\text{H}, ~C = 35~\mu \text{F}$
2. $R = 25~\Omega,~L= 2.5~\text{H}, ~C = 45~\mu \text{F}$
3. $R = 15~\Omega,~L= 3.5~\text{H}, ~C = 30~\mu \text{F}$
4. $R = 25~\Omega,~L= 1.5~\text{H}, ~C = 45~\mu \text{F}$

Step 1: Quality factor (Q) of an L

-

$-$ C

-

$-$ R circuit is given by,

Q = \frac{1}{R} \sqrt{\frac{L}{C}}

$Q = \frac{1}{R} \sqrt{\frac{L}{C}}$

where R is resistance, L is the inductance and C is the capacitance of the circuit.

Step 2: To make Q high, L should be high and C should be low.

These conditions are best satisfied by the values given in option (c).

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