1. Sequential Switching RC circuit RL circuits

2. Sequential switching ? Whenever switching occurs more than once in a circuit (RC or RL) Switch at position 1 for a long time and switched to 2 at t = 0 Switch at position 1 for a long time, switched to position 2 at t = t 2 and switch to position 3 at t=t 3 Example – non-sequential switching Example – Sequential switching

3. Sequential switching ? Whenever switching occurs more than once in a circuit (RC or RL) Example – non-sequential switching Switch at position 1 for a long time and switched to 2 at t = 0 Example – Sequential switching S1 has been opened and S2 has been closed for a long time. S1 closed at t = 0 and S2 opened at t = 0.5s

4. Sequential switching example Initially no energy in capacitor Switch at position 1 for a long time, switched to position 2 at t = t 2 and switched to position 3 at t = t 3 For t < t 2 since C initially has no energy then v c = 0

5. Sequential switching example Initially no energy in capacitor Switch at position 1 for a long time, switched to position 2 at t = t 2 and switched to position 3 at t = t 3 For t > t 2, v c will increase to the final value of V s. I

6. Sequential switching example Initially no energy in capacitor Switch at position 1 for a long time, switched to position 2 at t = t 2 and switched to position 3 at t = t 3 If switch is moved to 3 before the final value is reached, for t > t 3, v c starts to decay

7. Sequential switching example Three segments of equations is used to describe v c (i) For t < t 2 v c = 0 (ii) For t 2 < t < t 3 v c = V s (1– e -t/   (iii) For t > t 3 v c = V o3 e -t/  where V o3 = V s (1– e -t3/  