Question

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value

• A. The resonance frequency will increase
• B. The quality factor will increase
• C. The quality factor and the resonance frequency will remain constant
• D. The bandwidth of the resonance circuit will increase

Answer 1

The correct option is D

The bandwidth of the resonance circuit will increase

Explanation for the correct option:

Option D:

1. The bandwidth of a series LCR resonance circuit is given by $△B=\frac{R}{L}$ (Where R is the resistance and L is the inductance.)
2. According to the formula, $△B\propto R$
3. Hence, if resistance increases, the band width will also increase.
4. Therefore, this is the correct option.

Explanation for the incorrect options:

Option A:

1. The resonance frequency is given by ${\omega }_f=\frac{1}{\sqrt{LC}}$ (Where L is the inductance and C is the capacitance.)
2. Resonance frequency does not depend on the resistance.
3. Hence, there will be no effect on the resonance frequency if the resistance is increased.
4. Therefore, this is not the correct option.

Option B:

1. The Quality factor is given by $Q=\frac{\omega L}{R}$ (Where $\omega$ is the frequency, L is the inductance and R is the resisatnce)
2. From the formula, $Q\propto \frac{1}{R}$
3. Hence, the quality factor will decrease as the resistance increases.
4. Therefore, this is not the correct option.

Option C:

1. The quality factor decreases whereas the resonance frequency remains constant.
2. Therefore, this is not the correct option.

Therefore, option D is the correct option.