JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year ELECTRICAL CIRCUIT ANALYSIS Previous Question Paper (August/September - 2022 - R18)

The Reciprocity Theorem states that in any linear, bilateral, passive network, the ratio of the response (current or voltage) in one branch to the excitation (voltage or current) in another branch remains the same if the positions of the excitation and response are interchanged.

For a network with a single voltage source V in branch 1 producing a current I in branch 2, if the source is moved to branch 2, it will produce the same current I in branch 1. The network must not contain any dependent sources or non-linear elements. This theorem simplifies circuit analysis by allowing the calculation of transfer functions without re-solving the entire network.

To find the current i using nodal analysis, follow these steps:

1. Identify all nodes in the circuit and assign a reference node (ground) with a potential of 0V.
2. Assign unknown voltages (V1, V2, etc.) to the remaining non-reference nodes.
3. Apply Kirchhoff's Current Law (KCL) at each node, summing the currents leaving the node to zero.
4. Solve the resulting system of linear equations to determine the node voltages.
5. Calculate the branch current i using Ohm's Law, i = (V_a - V_b) / R, where V_a and V_b are the potentials at the ends of the branch containing the current i.

By setting up the nodal equations based on the specific resistance and source values provided in the circuit diagram, the matrix equation [G][V] = [I] is formed, where [G] is the conductance matrix, [V] is the vector of node voltages, and [I] is the vector of source currents. Solving this system yields the specific value for i.