Question

For the given nonlinear circuit, ????x = [???? ????x−1]/ 10 in which the units of ????x and ????x are V and A respectively. The source voltage is 3V and the source resistance is 1Ω.
Use graphical load-line techniques to solve for ????x and ????x. [Use a computer program to plot the characteristic curve and load line.]

Answer 1

$V_{x}$ = 0.75 V, $I_{x}$= 0.56 A

Explanation:

Given data:

$V_{s}$ = 3 V

$R_{s}$ = 1 Ω

$I_{x}$ = $\frac{3V_{X} }{4}$

Solution:

Using Kirchhoff's voltage law.

The law states that the algebraic addition of potential difference in loop is similar to zero.

$V_{s}$ - $I_{x}$$R_{s}$ - $V_{x}$ = 0

$V_{s}$ - $I_{x}$$R_{s}$ = $V_{x}$

3 - $\frac{3V_{X} }{4}$ × 1 = $V_{x}$

12 - 3$V_{x}$  = 4

3 - 3$V_{x}$  =

$V_{x}$ = 3/4

$V_{x}$ = 0.75 V

$I_{x}$ = $\frac{3V_{X} }{4}$

$I_{x}$ = $\frac{3}{4}$ × 0.75

$I_{x}$ = $\frac{2.25}{4}$

$I_{x}$ = 0.56 A.