Example 13. 5 kΩ a i 1 kΩ 1 kΩ 20 V 1 µF t=0 5 kΩ 10 µF b The circuit is in the steady state mode before the switch closes at t=0; Determine the current through terminal a and b i(t) for t>0. The circuit has two capacitors. Some beginners might try to combine the two capacitors to one. The two capacitors are not in parallel so we cannot combine the two capacitors. The circuit is a second order circuit. Here let us see if we can solve it by the methods we learned for the first order transient response. Let us consider the circuit before switching, vc1 (0 ) 10V vc 2 (0 ) 10V t>0 5 kΩ a i 1 kΩ 1 kΩ 20 V 1 µF 5 kΩ 10 µF b Immediately after the switching, a and b are shorted, the 20V source will drive a current through a and b. Also the voltage though each of the capacitors will drive the current flow from a to b. Let’s divide the problem into 3 sub problems. The current i can be considered as the superposition of three portions. t > 0 5 kΩ a a a i2 i1 i3 1 kΩ 1 kΩ 20 V 10 µF 1 µF b b b i1 (t ) 4mA i2 (0 ) 10mA 2 RC 1000 10 6 0.001 s i2 (t ) i2 (0 )e t / 10e 1000t mA i3 (0 ) 10mA 3 RC 1000 10 5 0.01s i2 (t ) i2 (0 )e t / 10e 100t mA i i1 (t ) i2 (t ) i3 (t ) 4 10e 1000t 10e 100t mA t 0