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Solved Problems-8

A coil under test is connected in series with a variable calibrated capacitor C and sine wave generator giving a 10 V r.m.s. output at frequency of 1000 rad/s. By adjusting C, the current in the circuit is found to be a maximum when C = 10.0 μF. Further, the current falls down to 0.707 times the maximum value when C = 12.5 μF.
  1. Find the inductance of the coil and resistance of the coil.
  2. Find the Q of the coil at 1000 rad/s
  3. What is the maximum current in the circuit?
Here, Vrms = 10 V, ω = 1000 rad/s,
C = 10 μF for maximum current (Imax)
= 12.5 μF for current Description: 3550.png
  1. Description: 3559.png
  2. At half-power frequency,
    Description: 3565.png; where, R is the resistance of the coil
    ∴ Description: 3571.png
    ∴ Quality factor of the coil, Description: 3577.png
  3. Maximum current in the circuit Description: 3594.png

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