A two-branch tuned circuit has a coil of resistance R and inductance L in one branch and capacitance C in the second branch. If R is increased, the dynamic resistance:a)may increase or decreaseb)decreasesc)remains constantd)increasesCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Dynamic resistance of a tuned circuit:

The value of the resistance at which the circuit becomes independent of frequency is known as the dynamic resistance.

Under such conditions the value of the time constant of two parallel branches becomes equal.

If the value of 'R' increases, then the dynamic resistance (R_d) decreases.

Answer

Dynamic resistance of a tuned circuit:

The value of the resistance at which the circuit becomes independent of frequency is known as the dynamic resistance.

Under such conditions the value of the time constant of two parallel branches becomes equal.

If the value of 'R' increases, then the dynamic resistance (R_d) decreases.

Answer

Introduction:
In a two-branch tuned circuit, one branch consists of a coil with resistance R and inductance L, while the other branch consists of a capacitor with capacitance C. The combination of these two branches forms a resonant circuit that can be used for various applications such as filtering and frequency selection.

Explanation:
When the resistance R in the coil branch is increased, the dynamic resistance of the tuned circuit decreases. This can be explained by the following points:

1. Quality Factor (Q Factor):
The quality factor of a tuned circuit is a measure of its efficiency and selectivity. It is defined as the ratio of the energy stored in the circuit to the energy dissipated in one cycle. The Q factor is given by the equation Q = ωL/R, where ω is the angular frequency.

2. Impedance and Dynamic Resistance:
The impedance of the tuned circuit is given by Z = R + j(ωL - 1/ωC), where j is the imaginary unit. The dynamic resistance is the real part of the impedance, i.e., Re(Z) = R.

3. Effect of Increased Resistance:
When the resistance R in the coil branch is increased, the dynamic resistance of the tuned circuit decreases. This can be understood by considering the equation for the Q factor. As R increases, the denominator of the Q factor equation increases, resulting in a decrease in the overall Q factor.

4. Implications:
The decrease in dynamic resistance has several implications for the performance of the tuned circuit. It affects the selectivity, bandwidth, and efficiency of the circuit. A lower dynamic resistance allows for a higher Q factor, which means that the circuit can store more energy and exhibit a sharper frequency response. This is desirable in applications where a narrow frequency range needs to be selected or filtered.

Conclusion:
In summary, when the resistance in the coil branch of a two-branch tuned circuit is increased, the dynamic resistance of the circuit decreases. This is due to the inverse relationship between resistance and the Q factor of the circuit. The decrease in dynamic resistance has implications for the selectivity, bandwidth, and efficiency of the circuit.

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