Category Archives: Electrical Circuits Problems

All Solved Problems in Electrical Circuits

Total Energy Stored - Circuit with Capacitors and Inductors


Find the total energy stored in the circuit.

find the energy stored in the circuit

Fig. (1-28-1) - The circuit



Solution
The circuit contains only dc sources. Recall that an inductor is a short circuit to dc and a capacitor is an open circuit to dc. These can be easily verified from their current-voltage characteristics. For an inductor, we have  v(t)=L \frac{d i(t)}{dt} . Since a dc current does not vary with time,  \frac{d i(t)}{dt}=0 . Hence, the voltage across the inductor is zero for any dc current. This is to say that dc current passes through the inductor without any voltage drop, exactly similar to a short circuit. For a capacitor, the current-voltage terminal characteristics is  i(t)=L \frac{d v(t)}{dt} . Voltage drop across passive elements due to dc currents does not vary with time. Therefore,  \frac{d v(t)}{dt}=0 and consequently the current of the capacitor is zero. This is to say that dc current does not pass through the capacitor regardless of the voltage amount. This is similar to the behavior of an open circuit. Please note that unlike dc current, ac current passes through capacitors in general.
Continue reading

Thévenin's Theorem - Circuit with Two Independent Sources


Use Thévenin's theorem to determine  I_O.

Thevenin's Theorem - Circuit containing two independent sources

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).
Continue reading

Thévenin's Theorem - Circuit with An Independent Source


Use Thévenin's theorem to determine  V_O .

A circuit with a voltage source

Fig. (1-26-1) - The Circuit



Solution
To find the Thévenin equivalent, we break the circuit at the  4\Omega load as shown below.
Continue reading

Superposition Method - Circuit With Dependent Sources


Determine  I_x ,  I_y and  V_z using the superposition method.

Superposition - Circuit with dependent sources

Solution
I. Contribution of the  -2V voltage source:
We need to turn off the current source by replacing it with an open circuit. Recall that we do not turn off dependent sources. The resulting circuit is shown below.
Continue reading

Superposition Problem with Four Voltage and Current Sources


Determine  V_x and  I_x using the superposition method.
A circuit with four voltage and current sources to be solved by the superposition method
Solution
I. Contribution of the  -5V voltage source:

To find the contribution of the  -5V voltage source, other three sources should be turned off. The  3V voltage source should be replaced by short circuit. The current source should be replaced with open circuits, as shown below.
Continue reading

Nodal Analysis - Circuit with Dependent Voltage Source


Determine the power of each source after solving the circuit by the nodal analysis.
Nodal Analysis - Supernode - Dependent Voltage Source 1

Answers:  P_{I_x}=0.497W, P_{1A}=-1.806W, P_{2A}=4.254W, P_{3V}=-3.87W, and  P_{5V}=-3.552W


Solution

I. Identify all nodes in the circuit.
The circuit has 6 nodes as highlighted below.
Continue reading