# Solve Using Current Division Rule

Find current of resistors, use the current division rule.

Suppose that $R_1=2 \Omega$, $R_2=4 \Omega$, $R_3=1 \Omega$, $I_S=5 A$ and $V_S=4 V$

Solution:
$R_2$ and $R_3$ are parallel. The current of $I_S$ is passing through them and it is actually divided between them. The branch with lower resistance has higher current because electrons can pass through that easier than the other branch. Using the current division rule, we get

# Mesh Analysis - Supermesh

Solve the circuit and find the power of sources:

$V_S=10V$, $I_S=4 A$, $R_1=2 \Omega$, $R_2=6 \Omega$, $R_3=1 \Omega$, $R_4=2 \Omega$.

Solution:
There are three meshes in the circuit. So, we need to assign three mesh currents. It is better to have all the mesh currents loop in the same direction (usually clockwise) to prevent errors when writing out the equations.

# Solve By Source Definitions, KCL and KVL

Find the voltage across the current source and the current passing through the voltage source.

Assume that $I_1=3A$, $R_1=2 \Omega$, $R_2=3 \Omega$, $R_3=2 \Omega$,$I_1=3A$, $V_1=15 V$,

Solution
$R_1$ is in series with the current source; therefore, the same current passing through it as the current source:

# 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 1-13: 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.

# Problem 1-9: Power of a Current Source

Find the power of $Is_1$ using circuit reduction methods.

Solution
$R_1$ and $R_4$ are parallel. $R_2$ and $R_3$ are also parallel. Therefore:

# Problem 1-8: Nodal Analysis - Power of Current Source

Solve the circuit using nodal analysis and find the power of $Is_1$.

Solution
a) Choose a reference node, label the voltages:

# Problem 1-2: Power and Conductance of Resistors

Determine the power absorbed by the resistors, the conductance of the resistors and $V$.

# Problem 1-1: Power of Elements

Find the power of each element. Which one is supplying power and which one is absorbing it?

Solution

a)  Passive sign convention, $P = V \times I = -8 W < 0$ supplying power.