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Solved Problems-16

Problems-16
A voltage of v = 2000 sin ωt + 400 sin 3 ωt + 100 sin 5 ωt is applied to a series circuit having R = 10 Ω and C = 30 μF and a variable inductance.
  1. Find the value of inductance so as to give resonance at 3rd harmonic frequency.
  2. What are the r.m.s. values of voltage and current with this inductance in circuit? Take ω = 300 rad/s.
Solution
Here, ω = 300 rad/s, R = 10 Ω, C = 30 × 10–6 F
 
∴ Resonant frequency ω0 = 3 × ω = 900 rad/s
  1. ∵ Description: 4816.png
  2.  
For 1st Harmonic (ω = 300 rad/s):
 
Description: 4822.png
 
∴ Description: 4831.png
 
∴ Description: 4837.png
 
For 3rd Harmonic (ω = 900 rad/s):
 
∴ Description: 4843.png
 
∴ Description: 4849.png
 
∴ Description: 4859.png
 
For 5th Harmonic (ω = 1500 rad/s):
 
Description: 4869.png
 
∴ Description: 4878.png
 
∴ Description: 4890.png
 
∴ RMS value of the current,
 
Description: 4903.png
 
∴ RMS value of the voltage,
 
Description: 4916.png
 




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