Q47 / 117 · NTA Abhyas (NEET) 2020 · Physics · Alternating Current

A $100 V,$ AC source of frequency $500 H z$ is connected to an $L C R$ circuit with $L = 8.1 m H$ ,
$C = 12.5 μ F$ , $R = 10 Ω$ all connected in series as shown in the figure. What is the quality factor of the circuit?

A
$2.02$
Correct answer
B
$2.54$
C
$50.54$
D
$200.54$

Solution

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

\Rightarrow Q = \frac{1}{10} \sqrt{\frac{8.1 \times 1 0^{- 3}}{12.5 \times 1 0^{- 6}}}

\Rightarrow Q = \frac{1}{10} \sqrt{\frac{81 \times 1 0^{3}}{125}}

\Rightarrow Q = \sqrt{\frac{81 \times 10}{25 \times 5}}

\Rightarrow Q = \frac{9 \times \sqrt{2}}{5} = 2.54

Hence, the correct answer is option: 'B'.

More Alternating Current Questions

If the voltage in the primary coil of a step-up transformer with a transformation ratio 3 : 2 is 30 V , then the voltage in the secondary co
A step-down transformer is used on a 1000 V line to deliver 20 A at 120 V at the secondary coil. If the efficiency of the transformer is 80
In a series L C R circuit, the voltage across resistance, capacitance and inductance is 10 V each. If the capacitor is removed, the voltage
A 100 V , AC source of frequency 500 Hz is connected to an LCR circuit with L = 8 . 1 mH , C = 12.5 µ F , R = 10 Ω all connected in series a
The current in an L C R circuit is given by I = 20 sin ⁡ 100 π t + π 3 A . The voltage across the inductance L of 0 .1 H at t = 0 will be
In the circuit shown in the figure, a conducting wire HE is moved with a constant speed v towards left. The complete circuit is placed in a