A Theorem on Power Superposition in Resistive Networks
Abstract : The superposition theorem, a particular case of the superposition principle, states that in a linear circuit with several voltage and current sources, the current and voltage for any element of the circuit is the algebraic sum of the currents and voltages produced by each source acting independently. The superposition theorem is not applicable to power, because it is a non-linear quantity. Therefore, the total power dissipated in a resistor must be calculated using the total current through (or the total voltage across) it. The theorem proposed and proved in this paper states that in a linear network consisting of resistors and independent voltage and current sources, the total power dissipated in the resistors of the network is the sum of the power supplied simultaneously by the voltage sources with the current sources replaced by open circuit, and the power supplied simultaneously by the current sources when the voltage sources are replaced by short-circuit. This means that the power is superimposed. The theorem can be used to simplify the power analysis of resistive networks.
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? It has been my experience that students require much practice with circuit analysis to become proficient. To this end, instructors usually provide their students with lots of practice problems to work through, and provide answers for students to check their work against.
? The ”wasted” time spent building real circuits will pay huge dividends when it comes time for them to apply their knowledge to practical problems.
? Furthermore, having students build their own practice problems teaches them how to perform primary research, thus empowering them to continue their electrical/electronics education autonomously.
• The theorem proposed and proved in this paper states that in a linear DC network consisting of resistors and independent voltage and current sources, the total power dissipated in the resistors of the network is the sum of the power supplied simultaneously by the voltage sources with the current sources replaced by open circuit, and the power supplied simultaneously by the current sources when the voltage sources are replaced by short-circuit.
• This means that the power is superimposed.
• Therefore, the total power dissipated in a resistor must be calculated using the total current through (or the total voltage across) it.
? They also need real, hands-on practice building circuits and using test equipment. So, I suggest the following alternative approach: students should build their own ”practice problems” with real components, and try to mathematically predict the various voltage and current values.
? This way, the mathematical theory ”comes alive,” and students gain practical proficiency they wouldn’t gain merely by solving equations.
? Another reason for following this method of practice is to teach students scientific method: the process of testing a hypothesis (in this case, mathematical predictions) by performing a real experiment.
? Students will also develop real troubleshooting skills as they occasionally make circuit construction errors.
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