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Solved Problems-4

Problems-4
Find the current i0 using superposition theorem.
  1. Description: Description: Description: 2230.png
  2. Description: Description: Description: 2236.png
  3. Description: Description: Description: 2242.png
Solution
  1. When voltage source is acting alone
The current in this case is, Description: Description: Description: 4610.png
 
Description: Description: Description: 2254.png
(i) Voltage source acting alone   (ii) Current source acting alone
 
When current source is acting alone
 
In this case, the current is, Description: Description: Description: 4616.png
 
∴ By superposition theorem, total current is,
 
Description: Description: Description: 4625.png 
  1. When dc source is acting alone
Equivalent impedance, Description: Description: Description: 4631.png
 
∴ main current, Description: Description: Description: 4637.png
 
Description: Description: Description: 2282.png
(i) dc source acting alone    (ii) ac source acting alone
 
∴ the current, Description: Description: Description: 4643.png
 
When ac source is acting alone
Equivalent impedance, Description: Description: Description: 4649.png
 
∴ main current, Description: Description: Description: 4655.png
 
∴ the current, Description: Description: Description: 4661.png
 
∴ by superposition theorem, total current is,
Description: Description: Description: 4667.png
  1. When the voltage source is acting alone
Equivalent impedance,
 
Description: Description: Description: 4673.png
 
Description: Description: Description: 1179.png
(i) Voltage source acting alone
 
∴ main current,
Description: Description: Description: 4685.png
 
Description: Description: Description: 4695.png
 
∴ The current, Description: Description: Description: 4701.png
 
When current source is acting alone
Description: Description: Description: 1208.png
 
Since Description: Description: Description: 4707.png
 
∴ The current, Description: Description: Description: 4713.png
 
Description: Description: Description: 4722.png
 
∴ By superposition theorem, total current is,
 
Description: Description: Description: 4743.png
 




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