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Solved Problems-15

Problems-15
  1. In the circuit shown in the figure, The switch S has been thrown to position 1 for a long period of time. Find the complete expression for the current after throwing the switch S to 2 which removes R1 from the circuit.
Description: Description: 10734.png
  1. If the values of VR1R2 and L be 10V, 1ohm, 2ohms and 1H respectively, calculate
    1. steady state current
    2. the energy stored in the inductance at steady state period
    3. time constant of the circuit for both the positions of the switch S
Also calculate the voltage across the resistor R2 and inductor L, at 0.05 second after the switch S has been thrown to position 2.
 
Solution
  1. For t < 0, as the circuit was in steady state with the switch in position 1, the circuit becomes as shown below.
∴ 
 
For t > 0, the circuit becomes as shown.
 
Description: Description: 3754.png
 
By KVL,
Description: Description: 8587.png
 
⇒ 
 
Taking inverse Laplace transform,
Description: Description: 8605.png
  1. V = 10 V, R1 = 1 ohm, R2 = 2 ohm and L = 1H
    1. Steady state current, Description: Description: 8634.png
    2. Energy stored in the inductance at steady state period,
       
      Description: Description: 8648.png
    3. Time constant of the circuit for switch in position 1 is,
       
      Description: Description: 8654.png 
Time constant of the circuit for switch in position 2 is,
Description: Description: 8660.png
 
For t = 0.05, voltage across the resistor,
Description: Description: 8673.png
and voltage across the inductor, Description: Description: 8679.png
 




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