P 8.6-16 Determine v(t) for t ≥ 0 for the circuit shown in Figure P 8.6-16.

Figure P 8.6-16

Let’s use source transformations to solve this circuit. First let’s convert the 2 A source and the 5 Ω resistor which is in parallel with it and get

Now we have the 5 Ω and 20 Ω resistors in parallel and can be replaced with

So the circuit now looks

Now source transform the 4 A supply

We can rearrange the left loop since everything is in series and we can add the two resistors and since the polarities are opposite we can subtract the two voltage supplies and our circuit looks like

Now do a source transformation on the voltage source and 9 Ω resistor and we get

Now we can add the 9 Ω and 18 Ω resistors are in parallel so we can replace them

So the circuit now looks

Now do a source transformation on the current supply and the 6 Ω resistor

Add the remaining two resistors which are in series and we have a circuit with our capacitor and a Thevenin circuit

So our Thevenin resistance is 10 Ω and at t = 0,

And after a long time in steady-state

So using standard form

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This page last updated on July 19, 2019