2.1 For the circuit shown in Figure 2(a), the switch was initially at Position 2: 2.1.1 Write the mathematical expressions for the transient behavior of the voltage ๐ฃ๐ and the current ๐๐ if the capacitor was initially uncharged and the switch is thrown into position 1 at ๐ก=0 s. (5) 2.1.2 Write the mathematical expressions for the voltage and the current if the switch is moved to position 3 at ๐ก=10 ms (assume no leakage current). (5) E 24V 8kฮฉ 0.08ยตF R1 R2 C 20kฮฉ iC vC + - 1 2 3 Figure 2(a) E 36V 8kฮฉ 2H R1 R2 L 4kฮฉ iL vL + - vR2 + - + vR1 - Figure 2(b) Figure 2: 2.2 For the circuit in Figure 2 (b): 2.2.1 The switch is closed at ๐ก=0 s. Write the mathematical expressions for ๐๐ฟ , ๐ฃ๐ฟ , ๐ฃ๐ 1 , ๐ฃ๐ 2 within five time constants of the storage phase. (5) 2.2.2 The switch is opened after five time constants of the storage phase, write the mathematical expressions for ๐๐ฟ , ๐ฃ๐ฟ , ๐ฃ๐ 1 , ๐ฃ๐ 2 . (5) [20]
Ctotal=
=
As switch is moved to position 1 at t=0, initially capacitor acts as a short circuit so Vc(0)=0v
ic(0)=
Time constant T=RC=20*0.47=0.96ms
As capasitors are charging from t=0;
is calculated at t= when capacitor acts as an open circuit, so
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