Understanding Duals in Electrical Circuits

In electrical circuits, the concept of duality is a powerful tool that relates two different circuits. If a circuit is described by equations, its dual circuit is described by the same equations but with voltages and currents swapped, and circuit elements replaced by their duals.

The fundamental idea is that many circuit theorems and analysis techniques have a dual counterpart. For instance, Kirchhoff's Voltage Law (KVL) is the dual of Kirchhoff's Current Law (KCL).

Dual Pairs of Circuit Elements and Sources

Specific circuit elements and sources have corresponding duals:

• Voltage source is the dual of a Current source.
• Current source is the dual of a Voltage source.
• An Inductor is the dual of a Capacitor.
• A Capacitor is the dual of an Inductor.
• A Resistor is the dual of a Conductor (or conductance).
• Series connection is the dual of Parallel connection.

Finding the Dual Pair

The question asks for the dual pair of the list: voltage source, current source, inductor, and capacitor. We need to find the dual of each item in the given order.

Let's find the dual of each component provided:

• Dual of Voltage source is Current source.
• Dual of Current source is Voltage source.
• Dual of Inductor is Capacitor.
• Dual of Capacitor is Inductor.

Therefore, the dual pair of (voltage source, current source, inductor, capacitor) is (Current source, voltage source, capacitor, inductor).

Comparing with Options

Let's compare this result with the given options:

Comparing the "Calculated Dual Pair" column with the options, we see that Option 3 matches our result: Current source, voltage source, capacitor and inductor.

Conclusion

The dual relationship swaps voltage and current roles and replaces elements with their duals. The dual of a voltage source is a current source, the dual of a current source is a voltage source, the dual of an inductor is a capacitor, and the dual of a capacitor is an inductor. Following this rule, the dual pair for (voltage source, current source, inductor, capacitor) is (current source, voltage source, capacitor, inductor).