Question

Which of the following combinations should be selected for better turning of an L.C.R circuit used for communication?
A) \[R=25\Omega ,L=1.5H,C=45\mu F\]
B) \[R=25\Omega ,L=1.5H,C=35\mu F\]
C) \[R=25\Omega ,L=2.5H,C=45\mu F\]
D) \[R=15\Omega ,L=3.5H,C=30\mu F\]

Answer 1

Hint: Using the formula of Q factor, Q factor is a non-dimension parameter which is used to state the under-dampness of an oscillator or resonator. It is defined as the highest energy stored in the resonator when energy is lost per cycle. The formula is:
\[Q=\dfrac{\sqrt{L}}{R\sqrt{C}}\]
where L is the unit of inductance, R is the resistance, C is the capacitance.

Complete step by step solution:
Let us do the question separately for each option by putting the value of R, L and C for all of them. By putting the value of R,L and C as:
\[Q=\dfrac{\sqrt{L}}{R\sqrt{C}}\]
We get the value of Q-factor as:
\[\Rightarrow Q=\dfrac{\sqrt{1.5}}{25\sqrt{45}}\]
\[\Rightarrow Q=7.3\]
Now moving onto the second option, we place the value of L, C and R into the formula as:
\[Q=\dfrac{\sqrt{L}}{R\sqrt{C}}\]
\[\Rightarrow Q=\dfrac{\sqrt{1.5}}{25\sqrt{35}}\]
\[\Rightarrow Q=8.28\]
After this we move onto the third option, we place the value of L, C and R into the formula as:
\[Q=\dfrac{\sqrt{L}}{R\sqrt{C}}\]
\[\Rightarrow Q=\dfrac{\sqrt{2.5}}{25\sqrt{45}}\]
\[\Rightarrow Q=9.43\]
After this we move onto the fourth option, we place the value of L, C and R into the formula as:
\[Q=\dfrac{\sqrt{L}}{R\sqrt{C}}\]
\[\Rightarrow Q=\dfrac{\sqrt{3.5}}{15\sqrt{30}}\]
\[\Rightarrow Q=13.67\]

Therefore, the value of the Q-factor is formed by that combination of L, C and R as \[Q=13.67\].

Note: The value of LCR is short form Inductance, Capacitance and Resistance respectively means that the circuit contains inductor, resistor and capacitance.