For what network Tellegen's theorem is valid?
2 Answers
Tellegen's theorem is valid for any electrical network, regardless of whether it is linear or nonlinear, active or passive. The theorem applies to:
1. **Linear Networks**: The theorem holds in networks where the relationships between voltages and currents are linear, following Ohm's law.
2. **Nonlinear Networks**: It can also be applied to nonlinear networks where the relationships between voltages and currents are nonlinear.
3. **Active and Passive Networks**: The theorem is applicable in both active networks (which include independent sources) and passive networks (which do not contain any sources).
4. **Bipolar Networks**: Tellegen's theorem is particularly noted for its application in bipole networks, which consist of branches that have two terminals.
The core idea of Tellegen's theorem is that the sum of the power in all the branches of the network at any given time is equal to zero, which can be expressed mathematically as:
\[
\sum (V_i \cdot I_i) = 0
\]
where \( V_i \) is the voltage across the \( i^{th} \) branch and \( I_i \) is the current through the \( i^{th} \) branch.
This universality makes Tellegen's theorem a powerful tool for analyzing complex electrical networks.
1. **Linear Networks**: The theorem holds in networks where the relationships between voltages and currents are linear, following Ohm's law.
2. **Nonlinear Networks**: It can also be applied to nonlinear networks where the relationships between voltages and currents are nonlinear.
3. **Active and Passive Networks**: The theorem is applicable in both active networks (which include independent sources) and passive networks (which do not contain any sources).
4. **Bipolar Networks**: Tellegen's theorem is particularly noted for its application in bipole networks, which consist of branches that have two terminals.
The core idea of Tellegen's theorem is that the sum of the power in all the branches of the network at any given time is equal to zero, which can be expressed mathematically as:
\[
\sum (V_i \cdot I_i) = 0
\]
where \( V_i \) is the voltage across the \( i^{th} \) branch and \( I_i \) is the current through the \( i^{th} \) branch.
This universality makes Tellegen's theorem a powerful tool for analyzing complex electrical networks.
Tellegen's theorem is valid for **any linear network**. This includes both electrical and non-electrical networks, as long as the network elements are linear and obey Ohm's Law.
In essence, Tellegen's theorem applies to:
1. **Electrical Networks**: Circuits composed of resistors, capacitors, inductors, and linear dependent sources.
2. **Mechanical Networks**: Systems involving linear springs and dampers.
3. **Thermal Networks**: Systems involving linear resistive thermal elements.
The theorem states that for any linear network, the algebraic sum of the power across all branches is zero. This principle holds regardless of the configuration of the network, provided the elements remain linear and the network is in a steady state.
In essence, Tellegen's theorem applies to:
1. **Electrical Networks**: Circuits composed of resistors, capacitors, inductors, and linear dependent sources.
2. **Mechanical Networks**: Systems involving linear springs and dampers.
3. **Thermal Networks**: Systems involving linear resistive thermal elements.
The theorem states that for any linear network, the algebraic sum of the power across all branches is zero. This principle holds regardless of the configuration of the network, provided the elements remain linear and the network is in a steady state.