P 2.2-5 The circuit shown in Figure P 2.2-5 consists of a current source, a resistor, and element A.

Consider three cases.

Figure P 2.2-5

Consider three cases.

(a) When element A is a 40-Ω resistor, described by i = v / 40, then the circuit is represented by

Determine the values of v and i. Notice that the above equation has a unique solution.

(b) When element A is a nonlinear resistor described by i = v² / 2, then the circuit is represented by

Determine the values of v and i. In this case there are two solutions of the above equation. Nonlinear circuits exhibit more complicated behavior than linear circuits.

(c)When element A is a nonlinear resistor described by i =0.8 + v² / 2, then the circuit is described by

Show that this equation has no solution. This result usually indicates a modeling problem. At least one of the three elements in the circuit has not been modeled accurately.

(a) When element A is a 40-Ω resistor, described by i = v / 40, then the circuit is represented by

Determine the values of v and i. Notice that the above equation has a unique solution.

Solve for v

Now find i

(b) When element A is a nonlinear resistor described by i = v² / 2, then the circuit is represented by

Determine the values of v and i. In this case there are two solutions of the above equation. Nonlinear circuits exhibit more complicated behavior than linear circuits.

Solve for v

Multiply equation by 10

Rearrange to standard quadratic form:

Use quadratic formula:

Now find i

Or

(c)When element A is a nonlinear resistor described by i =0.8 + v² / 2, then the circuit is described by

Show that this equation has no solution. This result usually indicates a modeling problem. At least one of the three elements in the circuit has not been modeled accurately.

Solve for v

Multiply equation by 2

Rearrange to standard quadratic form:

Use quadratic formula:

only has imaginary solutions so there is no real solution to this problem.

For Linear Model
For Non-Linear Model #1 For Or
For Non-Linear Model #2	No real Solutions!

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This page last updated on December 28, 2018