Test: Tellegen's Theorem - Electrical Engineering (EE) MCQ

• According to Tellegen’s theorem, the summation of instantaneous powers for the n number of branches in an electrical network is zero.
• Let n number of branches in an electrical network have I₁, I₂, I₃, ….. In respective instantaneous currents through them.
• These branches have instantaneous voltages across them are V₁, V₂, V₃, ….. Vn respectively.
• According to Tellegen’s theorem, 
• ∑ power delivered = ∑ power absorbed
• It is based on the conservation of energy.
• It is applicable to both linear and non-linear circuits.

Concept:
According to Tellegen’s theorem, the summation of instantaneous powers for the n number of branches in an electrical network is zero.
Let n number of branches in an electrical network have I₁, I₂, I₃, ….. In respective instantaneous currents through them.
These branches have instantaneous voltages across them are V₁, V₂, V₃, ….. V_n respectively.
According to Tellegen’s theorem, 
It is based on the conservation of energy.
It is applicable to both linear and non-linear circuits.
Analysis:
By applying Tellegen's theorem we can see that the net power developed in the circuit of the question = 0 watt

Tellegen theorem can be applied to any network- linear or non-linear, active or passive, time-variant, or time-invariant.
Tellegen Theorem: According to Tellegen’s theorem, the summation of instantaneous powers for the n number of branches in an electrical network is zero.
Let n number of branches in an electrical network have I₁, I₂, I₃, …. In respective instantaneous currents through them.
These branches have instantaneous voltages across them are V₁, V₂, V₃, …. Vn respectively.
According to Tellegen’s theorem:

It is based on the conservation of energy and is applicable to both linear and non-linear circuits.
Important Notes:
Various Theorem and the circuits where they are applicable is shown below in the table:

Tellegen’s Theorem:

Tellegen’s Theorem states that the summation of power delivered is zero for each branch of any electrical network at any instant of time.
Mathematically, for any linear, non-linear, passive, active, time-variant, or time-invariant network  this is defined as:

n = number of branches
v_k = voltage across the k^th element
i_k = current in the kth branch
Important Notes:
Various Theorem and the circuits where they are applicable is shown below in the table:

The circuit can be redrawn as:

Applying KCL at node VA, we get:

V_A = 4
Now, 
With I₂ + 3 = I₁
I₂ + 3 = 3
I₂ = 0 A
∴ Power delivered by the source = 10 x I₂ = 0W

Different theorems used in the electrical network:

1.Tellegen's Theorem
It states that the power consumed by all the passive elements is always equal to the power delivered by all active elements.
Hence, this theorem is a manifestation of the Law of Conservation of Energy.

2. Reciprocity Theorem:
It states that if the source and response of an electrical network are interchanged, then the parameters of the circuit remain the same.

3. Thevenin's Theorem:
It states that any linear circuit containing several sources and resistances can be replaced by just one single voltagesource in series with a single resistance connected across the load.

4. Norton's Theorem:
It states that any linear circuit containing several sources and resistances can be replaced by just one single current source in paralledwith a single resistance connected across the load.

Tellegen’s Theorem:

According to Tellegen’s theorem, the summation of instantaneous powers for the n number of branches in an electrical network is zero.
Let n number of branches in an electrical network have I₁, I₂, I₃, ….. In respective instantaneous currents through them.
These branches have instantaneous voltages across them are V₁, V₂, V₃, ….. V_n respectively.
According to Tellegen’s theorem,

It is based on the conservation of energy.

Important Points
Various Theorem and the circuits where they are applicable is shown below in the table:

Tellegen theorem can be applied to any network- linear or non-linear, active or passive, time-variant, or time-invariant.
Tellegen Theorem: According to Tellegen’s theorem, the summation of instantaneous powers for the n number of branches in an electrical network is zero.
Let n number of branches in an electrical network have I₁, I₂, I₃, …. In respective instantaneous currents through them.
These branches have instantaneous voltages across them are V₁, V₂, V₃, …. Vn respectively.

According to Tellegen’s theorem:

It is based on the conservation of energy and is applicable to both linear and non-linear circuits.

Important Points

Tellegen’s Theorem:
Tellegen’s Theorem states that the summation of power delivered is zero for each branch of any electrical network at any instant of time.
Mathematically, for any linear, non-linear, passive, active, time-variant, or time-invariant network  this is defined as:

n = number of branches
v_k = voltage across the k^th element
i_k = current in the k^th branch
KCL (Kirchoff Current Law): 
According to Kirchhoff’s current law (KCL), the algebraic sum of the electric currents meeting at a common point is zero.
Mathematically we can express this as:

Where in represents the nth current
M is the total number of currents meeting at a common node.
KCL is based on the law of conservation of charge.
KVL(Kirchhoff’s Voltage Law):
It states that the sum of the voltages or electrical potential differences in a closed network is zero. 
Mathematically we can express this as:

Where V_n represents the n^th Voltage
M is the total number of voltage element.
KVL is based on the law of conservation of energy.