Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Transcribed Image Text:### Superposition Theorem in Electrical Circuits
**Objective:** Use superposition to find the current \(i_0\). Additionally, determine the power consumed by the 12 Ohm resistor.
#### Circuit Description:
The circuit comprises:
- A 4.5 A current source.
- A 12Ω resistor.
- A 2Ω resistor.
- A 20 A current source.
- A 14Ω resistor.
- A 10Ω resistor.
- A 15Ω resistor.
- A 50 V voltage source.
These components are arranged as follows:
1. The 4.5 A current source is in series with the 12Ω resistor and the 2Ω resistor.
2. A 20 A current source is parallel to the series combination of the 4.5 A current source and the 2Ω resistor.
3. This combination is further in series with a 14Ω resistor which is parallel to a network containing a 10Ω resistor, a 50 V voltage source, and a 15Ω resistor.
The main objective is to determine the current \(i_0\) passing through the 12Ω resistor using the superposition technique and then find the power consumed by that resistor.
### Steps to Solve Using Superposition:
1. **Superposition Principle**:
- Temporarily remove all but one source (voltage and current sources) and solve the circuit.
- Repeat for each source.
- Combine the effects to get the total current \(i_0\).
2. **Removing Sources One at a Time**:
- Replace each independent voltage source with a short circuit (wire).
- Replace each independent current source with an open circuit (break).
3. **Calculating the Current \(i_0\)**:
- Open circuit the 20A current source and short circuit the 50V voltage source. Solve for \(i_0\) using the 4.5 A current source.
- Repeat the process for the other sources (one at a time).
- Superimpose the results.
4. **Determine Power Consumption**:
- Power consumed by the 12Ω resistor can be determined using \(P = i_0^2 \times R\).
### Graphical Representation:
- **Circuit Diagram**: The provided diagram represents the electrical circuit with components as described, with specified values of current and voltage sources and resistances.
#### Solving the Circuit:
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