P 5.3-10 The circuit shown in Figure P 5.3-10 has three inputs: v₁, v₂, and i₃. The output of the circuit is v_o. The output is related to the inputs by

v_o = av₁ + bv₂ + ci₃

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

Figure P 5.3-10

So we will deactivate all but one of the power sources and find what v₀ is

Deactivate v₂ and i₃ the circuit becomes

Since the 40 Ω and the 10 Ω resistors are in parallel we can replace them with an equivalent resistor and the voltage across the equivalent is still v₀

So the circuit now is

Now we can use voltage division and we find

Now deactivate v₁ and i₃ our circuit becomes

Again we can see 8 Ω and 40 Ω resistors are in parallel we can replace them with an equivalent resistor

and we can redraw the circuit as

Again we have two resistors in series so we can again do voltage division.

Now deactivate v₁ and v₂ Our circuit becomes

Again the 8 Ω and 40 Ω are in parallel but this time they are in parallel with the 10 Ω resistor, so we now have the circuit

This time we use current division to find the current in the 10 Ω resistor

Now putting these all together

Comparing that with

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This page last updated on February 28, 2019