# Duality (electrical circuits)

In electrical engineering, electrical terms are associated into pairs called **duals**. A dual of a relationship is formed by interchanging voltage and current in an expression. The dual expression thus produced is of the same form, and the reason that the dual is always a valid statement can be traced to the duality of electricity and magnetism.

Here is a partial list of electrical dualities:

- voltage – current
- parallel – serial (circuits)
- resistance – conductance
- impedance – admittance
- capacitance – inductance
- reactance – susceptance
- short circuit – open circuit
- Kirchhoff's current law – Kirchhoff's voltage law.
- Thévenin's theorem – Norton's theorem

## Contents

## History

The use of duality in circuit theory is due to Alexander Russell who published his ideas in 1904.^{[1]}^{[2]}

## Examples

### Constitutive relations

- Resistor and conductor (Ohm's law)

- Capacitor and inductor – differential form

- Capacitor and inductor – integral form

### Voltage division — current division

### Impedance and admittance

- Resistor and conductor

- Capacitor and inductor

## See also

## References

- Turner, Rufus P,
*Transistors Theory and Practice*, Gernsback Library, Inc, New York, 1954, Chapter 6.

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