P 8.6-27 When the input to the circuit shown in Figure P 8.6-27 is the voltage source voltage

v_s(t) = 3 – u(t) V

the output is the voltage

v_o(t) = 10 + 5 e^–50t V for t ≥ 0

Determine the values of R₁ and R₂.

Figure P 8.6-27

Annotating the circuit:

So we know the voltage across the capacitor is v_A. We can also see it is related to v₀ by voltage division.

Plug in for v₀

Now voltage across capacitor can be found from the standard form

The capacitor circuit in steady state is an open circuit so there is no voltage drop across resistor R₁ and the voltage across the capacitor is just the voltage of the supply v_s

So

Compare with the other expression

R₁ can be determined by comparing the argument of the exponential

We actually have two relations for R₂

and

Clearly these are the same, so solve R₂

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This page last updated on July 22, 2019