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  • A resistance  Inductance (L) = 2 henry and capacitance C = 5 mF

A resistance (\mathrm{R})=12 \Omega Inductance (L) = 2 henry and capacitance C = 5 mF are connected in series to an a.c. generator of frequency 50 Hz.

Option: 1

at resonance, the circuit impedance is zero


Option: 2

at resonance, the circuit impedance is 12 \Omega


Option: 3

the resonance frequency of the circuit is 1 / 2 \pi


Option: 4

theinductive reactance is less than the capacitive reactance


Answers (1)

best_answer

\mathrm{Given \mathrm{R}=12 \Omega, \mathrm{L}=2 \mathrm{H} and \mathrm{C}=5 \times 10^{-6} \mathrm{~F} }
The impedance of the circuit is given by
\mathrm{\begin{aligned} & \mathrm{Z}=\sqrt{\left[\mathrm{R}^2+\left(\omega \mathrm{L}-\frac{1}{\omega \mathrm{C}}\right)^2\right]}=\mathrm{R} \\ & \because \text { At resonance, } \omega \mathrm{L}=1 / \omega \mathrm{C} \\ & \therefore \mathrm{Z}=\mathrm{R}=12 \Omega \end{aligned} }

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mansi

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