P5.3-3 The circuit shown in Figure P5.3-3 has two inputs, v_s and i_s, and one output i_o. The output is related to the inputs by the equation

Given the following two facts:

The output is i_o = 0.45 A when the inputs are i_s = 0.25 A and v_s = 15 V.

and

The output is i_o = 0.30 A when the inputs are i_s = 0.50 A and v_s = 0 V.

Determine the values of the constants a and b and the values of the resistances are R ₁ and

R ₂.

Answers: a = 0.6 A/A, b = 0.02 A/V, R ₁ = 30 W and R ₂ = 20 W.

Figure P 5.3-3

To find the coefficients a and b we can use superposition, so we can first turn off the current source and the circuit becomes

Since we have a series circuit we can find by doing a voltage walk. Start below and go clockwise.

Solve for

So b must be

To get a we now shut off the voltage source and we have the circuit

This time we can do current division

So b must be

So now we have for

Now we can use the given facts or conditions

Solving the second equation we can find a

Now we can find b

Now we can use values of a and b we can find the two resistances

And

Solve for

Now solve for

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This page last updated on February 18, 2019