Solved Problems

Category: Resistive Circuits

Solved problems in resistive circuits such as nodal analysis, mesh analysis, superposition, source transformation, Thevenin and Norton theorems and so on

Nodal Analysis – Super-node: a Non-grounded Voltage Source

Use nodal analysis to solve the circuit and determine the values of $I_x$ and $V_y$ .

I. Identify all nodes in the circuit.
There are four nodes in the circuit:
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June 12, 2010
Nodal Analysis Problem with Dependent Voltage and Current Sources

Solve the circuit with the nodal analysis and determine $i_x$ and $V_y$ .

Solution
1) Identify all nodes in the circuit. Call the number of nodes $N$ .
The circuit has 5 nodes. Therefore, $N=5$ .
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June 11, 2010
Problem 1-16: Voltage Divider

Find $V_x$ (or $v_x(t)$ ) and $I_x$ (or $i_x$ ) using voltage division rule.
a)

b)

c)

d)

Solution

a)

Voltage divider: $V_x=\frac{5\Omega}{2\Omega+5\Omega}\times 14 V=10 V$
Ohm’s law: $I_x=\frac{V_x}{5 \Omega}=2 A$
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May 23, 2010
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

$V_{R_1}= Vs_1 = 10v \rightarrow P_{R_1}=\frac{V_{R_1}^2}{R_1}=50 W$
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April 23, 2010
Problem 1-11: Solving a Circuit with Three Nodes by the Nodal Analysis

Solve the circuit using nodal analysis and determine the power of $I_{s_1}$ .

Solution
I. Identify all nodes in the circuit. The circuit contains 3 nodes, as illustrated below.
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April 23, 2010
Problem 1-10: Solving by Nodal Analysis – Circuit with Four Nodes

Let’s use nodal analysis to solve this circuit and determine $V_a$ .

Solution
I. Identify all nodes in the circuit. There are four nodes in the circuit, as indicated below
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April 23, 2010
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:
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April 17, 2010
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:
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April 15, 2010
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:
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April 15, 2010
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:
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April 15, 2010