This document discusses Tellegen's theorem of circuit theory. It states that at any time t, the algebraic sum of the instantaneous power in n branches of a network equals zero if Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL) are satisfied. The document provides the mathematical statement of the theorem and proves it using a sample circuit where KCL and KVL are verified and the power in each branch is calculated to show that the total power supplied equals the total power dissipated.

1. CIRCUIT THEORY
TELLEGEN’S THEOREM
SYED HASAN SAEED
Sunday, August 18, 2019 1Syed Hasan Saeed

2. REFERENCE BOOKS
• Introductory Circuit Analysis, Robert L. Boylested, Pearson Education,
Prentice Hall.
• Networks And Systems, Ashfaq Husain, Khanna Book Publishing Co (P)
Ltd. Delhi.
• Networks And Systems, A Sudhakr, Shyammohan S Palli, Tata McGraw
Hill, New Delhi.
• Network Analysis, M.E. Van Valkenburg, PHI Learning Private limited,
New Delhi.
• Circuit Analysis Principle and Applications, Allan H. Robbins &Wilhelm
C. Miller, DELMAR CENGAGE Learning, Indian Reprint.
Sunday, August 18, 2019 syed hasan saeed 2

3. TELLEGEN‟S THEOREM
STATEMENT: This theorem states that “any time „t‟ the algebraic sum of
instantaneous power in „n‟ branches of any network is zero, if KCL and
KVL are satisfied.” Mathematically
PROOF: Consider the network shown in fig.1
Sunday, August 18, 2019 Syed Hasan Saeed 3
Fig. 1
0iv k
n
1k
k 
Z2
Z4
Z3Z1
i1
i3
i2
i4
v1 v3
v4v2v0
v1 = 6V, v2 = 4V,
v3 = 3V, v4 = 1V
i1 = 5A. i2 = 2A,
i3 = 3A, i4 = 3A
Where
Where vk = instantaneous voltage drop in
each branch
ik = instantaneous current in each branch

4. TELLEGEN‟S THEOREM
PROOF:
STEP 1 :Verification of KCL:
At node „a‟ : i1 = i2 + i3 (1)
5 = 2 +3 = 5
At node „b‟ : i3 =i4 (2)
3 =3
STEP 2 :Verification of KVL:
In mesh “1” : -v1 – v2 + v0 = 0
-6 -4 + 10 = 0
In mesh “2” : v2 – v3 – v4 = 0
4 – 3 – 1 = 0
Hence KVL and KCL are satisfied.
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5. TELLEGEN‟S THEOREM
STEP 3 : Calculation of Power in each branch
-v1 * i1 = -6 x 5 = -30 W -v4 * i4 = -1 * 3 = -3 W
-v2 * i2 = -4 * 2 = -8 W v0 * i1 = 10 * 5 = 50 W
-v3 * i3 = -3 * (-3) = -9 W
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0503-9-8-3-iv k
n
1k
k 
PROVED
OR,
Power Supplied = 50 W
Power Dissipated = - 50 W

6. Sunday, August 18, 2019 syed hasan saeed 6
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