What is the issue with connecting two ideal voltage sources of different voltages in parallel, and how should it be resolved in circuit analysis?

What is the issue with connecting two ideal voltage sources of different voltages in parallel, and how should it be resolved in circuit analysis?

• A. It is an invalid direct short between different voltage levels; resolve by introducing internal resistances or using Thevenin/Norton equivalents
• B. It is an issue for AC
• C. It leads to no current flow
• D. It creates a stable voltage of their average

Answer: (A)

When two sources that enforce different voltages are connected in parallel, the same node would have to be at two different voltage levels at the same time. In an ideal model, that cannot be satisfied, so the situation would produce an infinite or undefined current as the sources fight each other. In real life, sources have some finite internal resistance, which limits the current, but the parallel connection of ideal sources with different voltages is still not a valid configuration to rely on in analysis. To handle this in circuit analysis, replace each source with its Thevenin (or Norton) equivalent, including its internal resistance. Then you can analyze the network as if you have a single source with a particular voltage and series (internal) resistance. When you combine the two sources this way, the overall behavior is governed by the weighted average of the voltages, determined by the internal resistances, and the total resistance is the parallel combination of the two internal resistances. This approach shows why simply tying ideal sources of different voltages together is not a meaningful or solvable condition and how to resolve the issue using standard source-equivalent methods.

When two sources that enforce different voltages are connected in parallel, the same node would have to be at two different voltage levels at the same time. In an ideal model, that cannot be satisfied, so the situation would produce an infinite or undefined current as the sources fight each other. In real life, sources have some finite internal resistance, which limits the current, but the parallel connection of ideal sources with different voltages is still not a valid configuration to rely on in analysis.

To handle this in circuit analysis, replace each source with its Thevenin (or Norton) equivalent, including its internal resistance. Then you can analyze the network as if you have a single source with a particular voltage and series (internal) resistance. When you combine the two sources this way, the overall behavior is governed by the weighted average of the voltages, determined by the internal resistances, and the total resistance is the parallel combination of the two internal resistances. This approach shows why simply tying ideal sources of different voltages together is not a meaningful or solvable condition and how to resolve the issue using standard source-equivalent methods.