Test: Reciprocity Theorem - Electrical Engineering (EE) MCQ

Reciprocity Theorem:
Reciprocity theorem states that in any branch of a network, the current (I) due to a single source of voltage (V) elsewhere in the network is equal to the current through the branch in which the source was originally placed when the source is placed in the branch in which the current (I) was originally obtained.
The ratio of excitation to the response is constant.
E/R = K
Where,
E is excitation
R is response
K is constant
It is applicable for only single-source networks.

In-circuit (A), the value Ia is obtained for a voltage source V. According to the reciprocity theorem, this current is equivalent to Ib in a circuit (B).

The current I1 due to 16 V source only

The current I₂ due to 8 V source is, 

Total current:-
(4 + 0.66) = 4.66 A

Reciprocity theorem: It states that the current I in any branch of a network, due to single voltage source (E) anywhere in the network is equal to the current of the branch in which source was placed originally and when the source is again put in the branch in which current is obtained originally.

Limitations of reciprocity theorem:

• The network should be linear and time-invariant
• It can apply only to the single-source network

Reciprocity theorem states that in any branch of a network, the current (I) due to a single source of voltage (V) elsewhere in the network is equal to the current through the branch in which the source was originally placed when the source is placed in the branch in which the current (I) was originally obtained.

In the circuit (a), the value Ia is obtained for a voltage source V. According to reciprocity theorem, this current is equivalent to Ib in the circuit B.

Limitations of reciprocity theorem:

• The network should be bilateral linear and time-invariant.
• It can apply only to the single-source network and not for multi-source.
• It is also applicable for passive networks consisting L,C.
• Not applicable for circuits containing dependent sources even if it is linear.

Reciprocity Theorem:
In any passive linear bilateral network, if a single voltage source ‘V’ in the branch AB produces the current response ‘I’ in the branch CD, then the removal of voltage source from the branch AB and its insertion in the branch CD will produce same current ‘I’ in the branch AB.

In the reciprocity theorem, if the position of excitation and responses are interchanged, then their ratio remains the same.

Application:

I₂ = 1 A

Reciprocity Theorem:

• The reciprocity theorem states that the current at one point in a circuit due to a voltage at a second point is the same as the current at the second point due to the same voltage at the first.
• The reciprocity theorem is valid for all passive networks.

Reciprocity theorem:
Reciprocity theorem states that in any branch of a network, the current (I) due to a single source of voltage (V) elsewhere in the network is equal to the current through the branch in which the source was originally placed when the source is placed in the branch in which the current (I) was originally obtained.

In the circuit (a), the value Ia is obtained for a voltage source V. According to reciprocity theorem, this current is equivalent to Ib in the circuit B.

Limitations of reciprocity theorem:

• The network should be bilateral linear and time-invariant.
• It can apply only to the single-source network and not for multi-source.
• It is also applicable for passive networks consisting L,C.
• Not applicable for circuits containing dependent sources even if it is linear.

Reciprocity theorem:

Reciprocity theorem states that in any branch of a network, the current (I) due to a single source of voltage (V) elsewhere in the network is equal to the current through the branch in which the source was originally placed when the source is placed in the branch in which the current (I) was originally obtained.

The reciprocity theorem is the direct method of network analysis.

In circuit (a), the value Ia is obtained for a voltage source V. According to the reciprocity theorem, this current is equivalent to Ib in circuit B.
Limitations of reciprocity theorem:

• The network should be bilateral linear and time-invariant.
• It can apply only to the single-source network and not for multi-source.
• It is also applicable for passive networks consisting L,C.
• Not applicable for circuits containing dependent sources even if it is linear.
   

Reciprocity Theorem:
In any passive linear bilateral network, if a single voltage source ‘V’ in the branch AB produces the current response ‘I’ in the branch CD, then the removal of voltage source from the branch AB and its insertion in the branch CD will produce same current ‘I’ in the branch AB.

In reciprocity theorem, if the position of excitation and responses are interchanged, then their ratio remains the same.

Circuit 1: V₁ = 144 V, I₁ = 6 A
Circuit 2: V₂ = 144 V, I₂ = ?
According to reciprocity theorem,

Reciprocity Theorem:

• It states that In any branch of a network or circuit, the current due to a single source of voltage (V) in the network is equal to the current through that branch in which the source was originally placed when the source is again put in the branch in which the current was originally obtained.
• This theorem is used in the bilateral linear network which consists of bilateral components.
• In simple words, we can state the reciprocity theorem as when the places of voltage and current source in any network are interchanged the amount or magnitude of current and voltage flowing in the circuit remains the same.

The location of the voltage source and the current source may be interchanged without a change in current. However, the polarity of the voltage source should be identical to the direction of the branch current in each position.

In a balanced Wheatstone bridge, if the position of detector and source are interchanged, the bridge will still remain balanced. This inference is drawn from the Reciprocity theorem.