Which of the following combinations should be selected for better tuning of an circuit used for communication? [2016]

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Q.
Which of the following combinations should be selected for better tuning of an $L - C - R$ circuit used for communication [2016]

1 $R = 20 Ω, L = 1.5 H, C = 35 μ F$

2 $R = 25 Ω, L = 2.5 H, C = 45 μ F$

3 $R = 15 Ω, L = 3.5 H, C = 30 μ F$

4 $R = 25 Ω, L = 1.5 H, C = 45 μ F$

Ans.
(3)

Quality factor of an L-C-R circuit is given by,

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

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

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

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

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

Clearly $Q_{3}$ is maximum of $Q_{1}, Q_{2}, Q_{3}$ , and $Q_{4}$ .

Hence, option (3) should be selected for better tuning of an L-C-R circuit.

Solution

Q.
Which of the following combinations should be selected for better tuning of an $L - C - R$ circuit used for communication [2016]

1 $R = 20 Ω, L = 1.5 H, C = 35 μ F$

2 $R = 25 Ω, L = 2.5 H, C = 45 μ F$

3 $R = 15 Ω, L = 3.5 H, C = 30 μ F$

4 $R = 25 Ω, L = 1.5 H, C = 45 μ F$

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Solution

Q. Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication [2016]

1 R=20Ω,L=1.5H,C=35μF

2 R=25Ω,L=2.5H,C=45μF

3 R=15Ω,L=3.5H,C=30μF

4 R=25Ω,L=1.5H,C=45μF

Want Us to Email you About Special Offers & Updates?

Q.
Which of the following combinations should be selected for better tuning of an $L - C - R$ circuit used for communication [2016]

1 $R = 20 Ω, L = 1.5 H, C = 35 μ F$

2 $R = 25 Ω, L = 2.5 H, C = 45 μ F$

3 $R = 15 Ω, L = 3.5 H, C = 30 μ F$

4 $R = 25 Ω, L = 1.5 H, C = 45 μ F$