An inductor having a resistance of 25Ω and $Q_0$ of 10 at a resonant frequency of $10 kH_Z$ is fed from 100V supply. Calculate Value of series capacitance required to produce resonance with the coil. - The inductance of the coil. - $Q_0$ Using L⁄C ratio. - Voltage across capacitance - Voltage across coil.
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Mumbai University > FE > Sem 1 > Basic Electrical and Electronics Engineering

Marks: 7 M

Year: May 2013

Given:

$R = 25 Ω \\ Q_0=10 \\ f_0=10kH_Z \\ V = 100$

Solution:

$Q_0= \dfrac{V_c0}{V} \\ 10 = \dfrac{V_c0}{100} \\ V_{co}=1000V \\ I_0=\dfrac VR= \dfrac{100}{25}=4A \\ V_{co}= I_0 X_{co} 1000 = 4×X_{co} X_{co}=250 Ω$

But,

$X_{co}= \dfrac{1}{2πf_{oc}} \\ 250 = \dfrac{1}{2π×10×〖10〗^3×C} \\ C = 6.37 × 10^{-8} F \\ f_0= \dfrac{1}{2π\sqrt{LC}} \\ 10× 10^3= \dfrac{1}{2π\sqrt{L×6.37×10^{-8}}} \\ L = 3.98 mH \\ Q_0= \dfrac 1R \sqrt{\dfrac LC} \\ = \dfrac{1}{25} \sqrt{\dfrac{3.98×10^{-3}}{6.37×10^{-8}}}=10 \\ V_{LO}= V_{co}=1000V$