The input to the circuit shown in Figure P 10.10-11 is the voltage source voltage vs(t)

Chapter 10, Problem P10.10-11

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QUESTION:

The input to the circuit shown in Figure P 10.10-11 is the voltage source voltage \(v_x(t)\). The output is the voltage \(v_{\mathrm{o}}(t)\). The input \(v_{\mathrm{s}}(t)=2.5 \cos (1000 t) \mathrm{V}\) causes the output to be \(v_{\mathrm{o}}(t)=8 \cos \left(1000 t+104^{\circ}\right) \mathrm{V}\). Determine the values of the resistances \(R_1\) and \(R_2\).

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QUESTION:

The input to the circuit shown in Figure P 10.10-11 is the voltage source voltage \(v_x(t)\). The output is the voltage \(v_{\mathrm{o}}(t)\). The input \(v_{\mathrm{s}}(t)=2.5 \cos (1000 t) \mathrm{V}\) causes the output to be \(v_{\mathrm{o}}(t)=8 \cos \left(1000 t+104^{\circ}\right) \mathrm{V}\). Determine the values of the resistances \(R_1\) and \(R_2\).

ANSWER:

Step 1 of 4

The voltages  and  can be expressed as phasors:

The reactance  can be determined as follows:

 rad/s

The resistor  is connected in parallel with reactance .

The equivalent impedance is:

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