P5.3-1 The inputs to the circuit shown in Figure P5.3-1 are the voltage source voltages v₁ and v_2.. The output of the circuit is the voltage v_o. The output is related to the inputs by

v_o = a v₁ + b v₂

where a and b are constants. Determine the values of a and b.

Figure P 5.3-1

We use superposition, so shutting off a voltage source means replace the voltage source with a short circuit. When we consider the effect of only v₁, the circuit looks like

is the voltage across the 20 Ω resistor. The 20 Ω is in parallel with the 5 Ω resistor

So the circuit looks like

Use voltage division

Now deactivate and the circuit becomes

This time the two 20 Ω resistors are in parallel so the effective resistance is

So the circuit is

Again use voltage division

So adding these two results we have

So comparing with

Gives

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This page last updated on February 17, 2019