P 8.6-10 Determine the voltage v(t) for t ≥ 0 for the circuit shown in Figure P 8.6-10.

Figure P 8.6-10

The voltage v(t) is the voltage across the capacitor and it is also the voltage between points a and b. The voltage source changes, it is 5 V before t = 0, and it is 20 V after t = 0. To find

v_ab, we need to do a voltage walk from b to a. Adding some currents we can do mesh analysis to find this. The annotated circuit can be drawn as

then

Writing mesh equations

And

So now we can use the different values of v_s

and

For the Thevenin resistance our circuit looks like

This is two parallel resistors in series. So we have the 96 Ω in parallel with the 32 Ω resistor

So we now have

So we have these two in series and Thevenin resistance is

Again using the standard forumula

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This page last updated on July 17, 2019