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

  • Option 1)

    R = 20 \Omega,  L = 1.5 H,  C = 35 {\mu}F

  • Option 2)

    R = 25 \Omega,  L = 2.5 H,  C = 45 {\mu}F

  • Option 3)

    R = 15 \Omega,  L = 3.5 H,  C = 30 {\mu}F

  • Option 4)

    R = 25 \Omega,  L = 1.5 H,  C = 45 {\mu}F

 

Answers (1)

As we learnt in 

Q factor -

frac{1}{R}sqrt{frac{L}{C}}

- wherein

L - inductance

C - capacitance

 

  Quality factor of L-C-R circuit

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

Q _{1}=\frac{1}{20}\sqrt{\frac{1.5}{35\times 10^{-6}}}=50\times\sqrt{\frac{3}{70}}=10.35

Q _{2}=\frac{1}{25}\sqrt{\frac{2.5}{45\times 10^{-6}}}=40\times\sqrt{\frac{5}{90}}=9.43

Q _{3}=\frac{1}{15}\sqrt{\frac{3.5}{30\times 10^{-6}}}=\frac{100}{15}\times\sqrt{\frac{35}{3}}=22.77

Q _{4}=\frac{1}{25}\sqrt{\frac{1.5}{45\times 10^{-6}}}=\frac{40}{\sqrt{30}}=7.30

Clearly, Q is maximum of Q1 , Q and Q4

i.e for Q to be high, L should be high and C should be low.

 


Option 1)

R = 20 \Omega,  L = 1.5 H,  C = 35 {\mu}F

this is the incorrect option

Option 2)

R = 25 \Omega,  L = 2.5 H,  C = 45 {\mu}F

this is the incorrect option

Option 3)

R = 15 \Omega,  L = 3.5 H,  C = 30 {\mu}F

this is the correct option

Option 4)

R = 25 \Omega,  L = 1.5 H,  C = 45 {\mu}F

this is the incorrect option

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