1HINT Work to find vct first To make it more straightforward

1.)HINT: Work to find vc(t) first. To make it more straightforward, I recommend finding the Thevenin equivalent circuit for everything connected to the capacitor before solving for vc(t) for t>0. Then use ic(t)=C(dvc(t))/DT and Ohms law to find vo(t).

2.) Change the 6 kohm resistor to a 3 kohm resistor.

3.) Work to find iL(t) first. Then use Ohms law to find vo(t)

Solution

Thevenin\'s Theorem. Any combination of batteries and resistances with two terminals can be replaced by a single voltage source e and a single series resistor r. The value of e is the open circuit voltage at the terminals, and the value of r is e divided by the current with the terminals short circuited.

Worked Examples
Example 1:
The circuit shown in Figure 1b is the Thevenin equivalent circuit of the circuit shown in Figure 1a. Find the value of the open circuit voltage, Voc and Thevenin resistance, Rth.

Solution: The circuit from Figure 1a can be reduced to its Thevenin equivalent circuit in four steps shown in Figure 2a, b, c and d.
A source transformation transforms the series voltage source and 20 resistor in Figure 1a into the parallel current source and 20 resistor in Figure 2a. The current source current is calculated from the voltage source voltage and resistance as 20 V1 A20 =. After the source transformation, the 20 resistor is parallel to the 80 resistor. Replacing these parallel resistors with the equivalent 16 resistor produces the circuit shown in Figure 2b.