# 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.

# 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 1-11: Solving a Circuit with Three Nodes by the Nodal Analysis

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

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

# Problem 1-10: Solving by Nodal Analysis - Circuit with Four Nodes

Solve the circuit by nodal analysis and find $V_a$.

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

# 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 1-7: Circuit Reduction - Current Divider

Find $I_9$ (Hint: use circuit reduction).
All resistors are $10\Omega$ and $Is_1=10A$

Solution
Let's redraw the circuit:

# Problem 1-6: Single Node-Pair Analysis

Find $I_1$ using single node-pair analysis (do not reduce the circuit).

$Is_{1}=1A,\, Is_{2}=2A,\, Is_{3}=3A,\, R_1=2 \Omega,\, R_2=4\Omega$ and $R_3=4\Omega$.

Solution
a) Redraw the circuit if necessary. Mark the voltage across nodes:
Find $V_2$ using single loop analysis (do not reduce the circuit).
$Vs_{1}=2v,\, Vs_{2}=2v,\, Vs_{3}=2v,\, R_1=1 \Omega,\, R_2=2\Omega$ and $R_3=4\Omega$.