 #1
JessicaHelena
 188
 3
 Homework Statement:

A linear circuit containing two voltage dependent sources, as shown. The elements in this circuit have the following values: ##R_1 = 7.2k## Ohms, ##R_2 = 12k## Ohms, ##R_3 = 3.3k## Ohms, ##\alpha = 0.025## A/V and ##\beta = 5##.
Calculate the numerical value for the Thevenin equivalent resistance for terminal AB.
 Relevant Equations:
 KVL and KCL
I am having a hard time solving this. Letting \$i\$ be the current flowing into ##R_3##, ##i_1## the current flowing through ##R_1## and ##i_2## the current through ##R_1##—and the node between R3 and R1 be e_1;
Using KVL and KCL, I've managed to find that
##i + I = i_1 + i_2##
Hence ##\frac{e_1\beta v_2}{R_3} + \alpha v_1 = \frac{v_2}{R_2} + \frac{v_1}{R_1}##
also from one of the loops around V, R3 and R2, I have ##e_1  2\beta v_2 + v_2 = 0##.
I have 3 unknowns so far, so I'm trying to find another equation, but I'm not sure what to do from here.
Using KVL and KCL, I've managed to find that
##i + I = i_1 + i_2##
Hence ##\frac{e_1\beta v_2}{R_3} + \alpha v_1 = \frac{v_2}{R_2} + \frac{v_1}{R_1}##
also from one of the loops around V, R3 and R2, I have ##e_1  2\beta v_2 + v_2 = 0##.
I have 3 unknowns so far, so I'm trying to find another equation, but I'm not sure what to do from here.