Problema 14-7    Source:    Adapted from Problem 5.3-13 - page 207 -    SVOBODA, James A. & DORF, Richard C. -    Book: Introduction to Electric Circuits - 9th edition - Ed. Wiley - 2014.

The input to the circuit shown in Figure 14-07.1 is the current source I₁. The output is the voltage V₀. The current source I₂ is used to adjust the relationship between input and output. Determine the values of I₂ and R so that the output is related to the input by the equation below:

Solution of the Problem 14-7   -    Superposition Method

Initially we must realize that the two 8 Ω resistors are connected in parallel. Therefore, we can replace them with a 4 Ω resistor. And the 4 Ω and R resistors are also connected in parallel. Using the Superposition theorem we will write the equation of V₀ ignoring the current source I₂ (it will be an open circuit). So, we have:

Now let's write the equation for V₀ ignoring the current source I₁ (it will be an open circuit). So, we have:

Remembering that by the Superposition theorem the final result is the sum of the partial results, so we have:

This result can be compared with the equation in the problem statement and, equating similar terms, we can easily see that for the first installment we can write:

Canceling the term I₁ we can find the value of R, because:

Solving this equation we find the value of R, or:

Now equating the second installment of the two equations, we obtain:

Solving this equation we find the value of I₂, or: