A series LCR circuit has inductance and an unknown capacitance

PHYSICS · Multi-part · CBSE · Physics · Alternating Current · Alternating Current

Problem

A series LCR circuit has inductance

L=40\,\text{mH}

and an unknown capacitance

C

. When the angular frequency of the applied source is steadily increased, the current amplitude shows the following behaviour: • at

4800\,\text{rad s}^{-1}

I=1.90\,\text{A}

• at

5000\,\text{rad s}^{-1}

I=2.05\,\text{A}

• at

5200\,\text{rad s}^{-1}

I=1.90\,\text{A}

No value of

\omega

beyond this range gives a larger current than

2.05\,\text{A}

. (i) By suitable interpolation, estimate the resonant angular frequency

\omega_0

and the maximum current

I_{\text{max}}

. (ii) Using the data above, find the angular frequencies at which the current is

I_{\text{max}}/\sqrt{2}

, and hence compute the bandwidth

\Delta\omega

. (iii) Evaluate the quality factor

Q

and obtain the numerical value of the capacitance

C

. (iv) If a resistor of

5\,\Omega

were added in series to the existing resistance, predict qualitatively how the resonance curve would change with respect to height and width.