Tellegen's Theorem Formula |
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| \( \textstyle \sum_{k=1}^b V_k \cdot I_k \;=\; 0 \) | ||
| Symbol | English | Metric |
| \( \textstyle \sum_{k=1}^b \) = Sum of the Terms from k=1 to k=b | \(dimensionless\) | \(dimensionless\) |
| \( b \) = Number of Branches in the Electric Network | \(dimensionless\) | \(dimensionless\) |
| \( V_k \) = Voltage across Branch k | \(V\) | \(V\) |
| \( I_k \) = Current across Branch k | \(A\) | \(A\) |
Tellegen's theorem is a principle in electrical network theory that applies to any linear or nonlinear, time-invariant or time-varying network with a consistent topology. It states that in any network, the sum of instantaneous powers consumed by various elements in various branches is always equal to zero, provided the network obeys Kirchhoff's laws.
This implies that the total power delivered by sources within the network equals the total power absorbed by all other elements, reflecting conservation of energy. The theorem is versatile, applicable to both DC and AC circuits, and is derived from Kirchhoff's current law and Kirchhoff's voltage law. It is widely used in circuit analysis, network synthesis, and sensitivity analysis, providing a powerful tool for verifying the consistency of network solutions and understanding power flow.
