To find the total power developed in a circuit, one must first verify the circuit's validity, then apply Kirchhoff's rules to calculate currents and, subsequently, power. The calculated power values must align with the conservation of charge and energy principles and check as reasonable within the context of the circuit.
To determine the total power developed in a circuit, the validity of the interconnection must be assessed first. If a circuit cannot be reduced to series and parallel connections, Kirchhoff's rules come into play. These rules are based on the principles of conservation of charge and energy.
When analyzing the circuit, locate the junctions without concern for the current direction and apply Kirchhoff's junction rule—essentially the law of conservation of charge, which states that the sum of currents entering a junction equals the sum of currents leaving the junction. Similarly, Kirchhoff's loop rule, which is the law of conservation of energy, ensures that the total voltage around any closed loop of the circuit must be zero.
After computing the currents in the circuit, calculate the power dissipated by the resistors (using P = I^2R for each resistor) and the power supplied by the voltage sources. The combined power calculated must be consistent with the energies supplied and dissipated.
Any resulting values that are unrealistically large or small, or if resistances are negative, indicate that the analysis is likely flawed. Finally, ensure that the computed values satisfy both Kirchhoff's rules. A valid interconnection should satisfy the equations derived from these rules, including the junction and loop rules, thus confirming the total power developed by the circuit.