DP 5-1 The circuit shown in Figure DP 5-1a has four unspecified circuit parameters: vs, R1, R2, and R3. To design this circuit, we must specify the values of these four parameters. The graph shown in Figure DP 5-1b describes a relationship between the current i and the voltage v. Specify values of vs, R1, R2, and R3 that cause the current i and the voltage v in

Figure DP 5-1a to satisfy the relationship described by the graph in Figure DP 5-1b.

First Hint: The equation representing the straight line in Figure DP 5-1b is

That is, the slope of the line is equal to –1 times the Thévenin resistance and the “vintercept” is equal to the open-circuit voltage.

Second Hint: There is more than one correct answer to this problem. Try setting R1 = R2.

Figure DP 5-1

First determine the equation of the line. Use the two point form of a line

Use the points (0, 5) and (8, 0) 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

This is R₁ and R₂ in parallel and then in series with R₃

So

We have one condition on Resistors. Next consider the open circuit voltage

The open circuit voltage is the voltage across R₂, which we can get from voltage division

Now comparing with the equation we found from the graph we have the following two conditions.

And

Applying hint 2, R1 = R2

Again apply hint 2

Choose

One possible solution

Another possible solution

Other Solutions possible

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This page last updated on March 9, 2019