Question 2.35: An inductive coil has a resistance of 10 Ω and inductance of...
An inductive coil has a resistance of 10 Ω and inductance of 100 mH. This coil is connected in parallel with a capacitor of 20 μF. A variable frequency power at 100 V is applied across this parallel circuit. Calculate the frequency at which the circuit will reasonate. Also calculate the Q-factor, dynamic impedance of the circuit, and resonant current.
Resonant frequency, f_{0}=\frac{1}{2π}\sqrt{\frac{1}{LC} – \frac{R²}{L²}}
Substituting the given values,
=112.48 Hz
Q-factor = \frac{2πf_{0}L}{R}=\frac{6.28 × 112.48 × 100 × 10^{-3}}{10} = 7.06
Dynamic impedance, Z_{0}=\frac{L}{CR}=\frac{100 × 10^{-3}}{20 × 10^{-6} × 10}= 500 Ω
Current at resonance, I_{0}=\frac{V}{Z_{0}}=\frac{100}{500} = 0.2 A