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Solved Problems-15

Problems-15
Determine the resonant frequency, the source current and the input impedance for the circuit shown in figure for each of the following cases:
 
 
Case I RL = 150 Ω RC = 100 Ω
 
Case II RL = 150 Ω RC = 0 Ω
 
Case III RL = 0 Ω RC = 0 Ω
 
Solution
Case I: Here RL = 150 Ω, L = 0.24 H, RC = 100 Ω, and C = 3 μF
 
Resonant frequency,
Description: 4507.png
 
Reactances at this frequency,
 
Description: 4526.png
 
Description: 4605.png
 
∴ Description: 4611.png
 
 
and Description: 4623.png
 
∴ Total source current,
 
Description: 4631.png
 
∴ Input impedance Description: 4637.png
 
Case II: Here RL = 150 Ω, L = 0.24 H, RC = 0, and C = 3 μF
 
Resonant frequency,
Description: 4643.png
 
Reactances at this frequency,
Description: 4652.png
 
Description: 4658.png
 
∴ Description: 4664.png
 
and Description: 4670.png
 
∴ Total source current, Description: 4676.png
 
∴ Input impedance Description: 4682.png
 
Case III: Here RL = 0, L = 0.24 H, RC = 0, and C = 3 μF
 
Resonant frequency,
 
Description: 4688.png
 
Reactances at this frequency,
 
Description: 4779.png
 
Description: 4786.png
 
∴ Description: 4792.png
 
and Description: 4798.png
 
∴ Total source current, Description: 4804.png
 
∴ Input impedance Description: 4810.png
 




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