Question

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication ?

• A. $R =20\, \Omega, L =1.5 H , C =35\, \mu F$
• B. $R = 25 \Omega, L = 2.5 H , C = 45\, \mu F$
• C. $R = 15 \Omega, L = 3.5 H , C = 30 \mu F$
• D. $R = 25 \Omega, L = 1.5 H , C = 45 \mu F$

Answer 1

The Correct Option is C

The resonance frequency of an L-C-R circuit is given by the formula:

f_r = \frac{1}{2\pi \sqrt{L \cdot C}}

The quality factor (Q) for an L-C-R circuit is given by:

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

For better tuning, a high value of Q factor is desired, which implies minimizing resistance (R) along with appropriately balancing the inductance (L) and capacitance (C) to achieve resonance at the desired frequency.

Let's evaluate each option to find the combination that provides the best Q factor:

• R = 20 \Omega, L = 1.5\, \text{H} , C = 35\, \mu \text{F}
• R = 25 \Omega, L = 2.5\, \text{H} , C = 45\, \mu \text{F}
• R = 15 \Omega, L = 3.5\, \text{H} , C = 30\, \mu \text{F}
• R = 25 \Omega, L = 1.5\, \text{H} , C = 45\, \mu \text{F}

The correct answer is the one with R = 15 \Omega, L = 3.5\, \text{H} , C = 30\, \mu \text{F} since:

• This combination has the minimum resistance value, which will maximize the Q factor.
• A higher inductance value (L = 3.5\, \text{H}) and balanced capacitance (C = 30\, \mu \text{F}) make the circuit better suited for tuning.

Hence, this combination should be selected for better tuning of an L-C-R circuit used for communication.