Find values of I and R such that the circuit in is equivalen

Find values of I and R such that the circuit in is equivalent to the circuit in (a). This circuit is referred to as the Thevenin Equivalent circuit to the circuit in (a). Find the open circuit voltage, V_oc using KCL (I_1 + I_2 + I_3 = 0) and KVL (voltage around a loop must sum to zero). Find the equivalent resistance, R_TH, by setting voltage sources to short circuits and current sources to open circuits.

Solution

from figure (a), apply KCL

I1+I2+I3=0

from the circuit I2=8 amps.

(Vout-2)/2+8+Vout/2=0

Vout-1+8=0

Vout=-7 volts.

Rth:

voltage source is short circuited and current source is open circuited

Rth=(2*2)/(2+2)+3=1+3=4 ohms.