# 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:

# 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:

# 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 1-12: Using Voltage Sources to Determine Node Voltages

Determine the power of $R_1, R_2$ and $Vs_1$. (Hint: there is no need to use nodal analysis; voltages between nodes can be easily found by the voltage sources.)

Solution

$V_{R_1}= Vs_1 = 10v \rightarrow P_{R_1}=\frac{V_{R_1}^2}{R_1}=50 W$

# 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.