P 5.3-13 The input to the circuit shown in Figure P 5.3-13 is the current i₁. The output is the voltage v₀. The current i₂ is used to adjust the relationship between input and output. Determine values of current i₂ and resistance R, that cause the output to be related to the input by the equation

Figure P 5.3-13

If we deactivate i₂ the circuit becomes

We can simplify this circuit by adding the R and 4 Ω resistor in parallel and the two 8 Ω resistors are in parallel. So we find the two effective resistors

Putting these in our circuit becomes

So

- sign due to polarization provided. We find i_2Ω from current division

If we deactivate i₁ the circuit becomes

We still have the two pairs of parallel resistors so the circuit becomes

So

This time polarization gives us a + sign. We find i_2Ω from current division

comparing

This yields equations

And

The first equation gives us R

Now we plug that in to second equation and we can solve for i₂

Solving for i₂

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This page last updated on February 28, 2019