DP 5-2 The circuit shown in Figure DP 5.2a has four unspecified circuit parameters: is, R1, R2, and R3. To design this circuit, we must specify the values of these four parameters. The graph shown in Figure DP 5-2b describes a relationship between the current i and the voltage v. Specify values of is, R1, R2, and R3 that cause the current i and the voltage v in Figure DP5-2a to satisfy the relationship described by the graph in Figure DP 5-2b.

First Hint: Calculate the open-circuit voltage, voc, and the Thévenin resistance, Rt, of the part of the circuit to the left of the terminals in Figure DP 5-2a.

Second Hint: The equation representing the straight line in Figure DP 5-2b is

That is, the slope of the line is equal to –1 times the Thévenin resistance and the

“v-intercept” is equal to the open-circuit voltage.

Third Hint: There is more than one correct answer to this problem. Try setting both R3 and R1 +R2 equal to twice the slope of the graph in Figure DP 5-2b.

Figure DP 5-2

First let’s get the equation from the plot. Use two point form of line.

Use the points (-6, 0) and (0, -3) as the two points.

Now compare with equation

We can identify

Since the units are Volts/mA these are kΩ

and

Now to get Rt we would deactivate the power source and we would have

We have R₁ and R₂ in series so we add them and then they are in parallel with R₃ so we get

So

From result above first condition is

To find open circuit voltage we have

We can find the current in i₃ by using current division

So is

Our second condition is

Recall Third Hint: There is more than one correct answer to this problem. Try setting both R3 and R1 +R2 equal to twice the slope of the graph in Figure DP 5-2b.

This means

Try

Check R_t

Using the other condition we can get i_s

One possible solution

Another possible solution

Other Solutions possible

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This page last updated on March 9, 2019