Superposition Circuits: Approach to Solving

[Jason03]

I was looking to an approach for this problem below...

http://img389.imageshack.us/img389/9387/screenshot003yw2.png

 

[CEL]

Use superposition.
With the dc source, the inductor is a short circuit and the capacitor is an open circuit.
With the ac source the inductor impedance is $$j\omega L$$ and the capacitor impedance is $$\frac{1}{j\omegaC}$$.

 

[piercas]

Superposition circuits are a commonly used method for solving complex electrical problems. This approach involves breaking down the circuit into smaller, simpler circuits and analyzing them individually. Each smaller circuit is analyzed using the principle of superposition, which states that the total current or voltage in a circuit is equal to the sum of the individual currents or voltages from each source.

In the problem provided, the circuit can be broken down into three simpler circuits: the top left loop, the top right loop, and the bottom loop. By analyzing each of these circuits separately and using the principle of superposition, the total current through the 20 ohm resistor can be determined.

First, consider the top left loop. Since the 10V source is connected to the 20 ohm resistor and the 5 ohm resistor is not connected to any other source, the current through the 20 ohm resistor is simply 10V/20 ohm = 0.5A.

Next, consider the top right loop. In this case, the 5 ohm resistor is connected to both the 10V and 5V sources. Using the principle of superposition, we can calculate the current through the 20 ohm resistor from the 10V source and the current from the 5V source separately. The current from the 10V source can be calculated as 10V/5 ohm = 2A, while the current from the 5V source is 5V/5 ohm = 1A. Therefore, the total current through the 20 ohm resistor from the top right loop is 2A + 1A = 3A.

Finally, consider the bottom loop. Similar to the top left loop, the 5 ohm resistor is not connected to any other source, so the current through the 20 ohm resistor is again 0.5A.

Now, we can add up the currents from each loop to determine the total current through the 20 ohm resistor. Using Kirchhoff's Current Law, we know that the current entering the 20 ohm resistor must be equal to the current leaving it. Therefore, the total current is 0.5A + 3A + 0.5A = 4A.

In conclusion, the superposition approach allows us to solve complex circuits by breaking them down into simpler circuits and using the principle of superposition to calculate the total current or voltage. It is