# Find Thevenin's and Norton's Equivalent Circuits

Find Thevenin's and Norton's Equivalent Circuits:

Suppose that $R_1=5\Omega$, $R_2=3\Omega$ and $I_S=2 A$.

# Solution

The circuit has both independent and dependent sources. In these cases, we need to find open circuit voltage and short circuit current to determine Norton's (and also Thevenin's) equivalent circuits.

# Find Voltage Using Voltage Division Rule

Determine voltage across $R_2$ and $R_4$ using voltage division rule.
Assume that
$V_1=20 V$, $R_1=10 \Omega$, $R_2=5 \Omega$, $R_3=30 \Omega$ and $R_4=10 \Omega$

Solution:
Please note that the voltage division rule cannot be directly applied. This is to say that:

# Thévenin's Theorem - Circuit with Two Independent Sources

Use Thévenin's theorem to determine $I_O$.

Fig. (1-27-1) - Circuit with two independent sources

Solution
Lets break the circuit at the $3\Omega$ load as shown in Fig. (1-27-2).
Use Thévenin's theorem to determine $V_O$.
To find the Thévenin equivalent, we break the circuit at the $4\Omega$ load as shown below.