# 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).

# Ideal Independent Sources

1) Ideal Independent Voltage Sources
An ideal independent voltage source is a two-terminal circuit element where the voltage across it
a) is independent of the current through it
b) can be specified independently of any other variable in a circuit.
There are two symbols for ideal independent voltage source in circuit theory:

Symbol for Constant Independent Voltage Source

# Problem 1-15: Power of Independent Sources

Determine the power of each source.
a)

b)

Solution
a) The current source keeps the current of the loop $2A$ and the voltage source keeps the voltage across the current source $3v$ as shown below.

# Problem 1-14: Current of A Voltage Source

Find the current passing through the voltage source:
a)

b)

Solution
a) The voltage source is in series with the current source. Since by definition a current source keeps the current passing through itself constant and the voltage source is in series with the current source, it should have the same current $10 A$ .

# Problem 1-13: Voltage of A Current Source

Find voltages across the current sources.
a)

b)

c)

d)

e)

Solution

In each case, the current source is parallel with a voltage source. Therefore, the voltage across the current source is equal to the voltage of the voltage source, regardless of other elements.