Govt. Exams
Entrance Exams
For a circuit with m independent loops (meshes), exactly m independent mesh equations are required. Each mesh contributes one independent equation. Therefore, for 3 loops, 3 equations are needed.
Number of independent mesh equations equals the number of independent loops (meshes) in the circuit. For m meshes, we need exactly m independent KVL equations.
This is Euler's formula for planar networks: Number of independent loops (L) = Number of branches (B) - Number of nodes (N) + 1. This is fundamental in mesh analysis.
Superposition theorem applies to linear networks and can be used to find voltage and current, but NOT power (since power is non-linear function).
Maximum power transfer theorem states that maximum power is transferred when load resistance equals the Thevenin equivalent resistance of the source (2Ω in this case).
In nodal analysis, we need (n-1) independent KCL equations for n nodes, where one node is taken as reference (ground). This follows from the fact that one equation is dependent on others.
Removing all independent sources leaves only passive elements (resistors), making the network passive with no energy supply capability.
Active elements (voltage/current sources) can supply power. Passive elements (R, L, C) can only dissipate or store energy.
Number of mesh current variables equals the number of independent meshes in the circuit. For 3 independent meshes, we have 3 mesh currents (I₁, I₂, I₃).
At Wheatstone bridge balance: R₁/R₂ = R₄/R₃ or R₁×R₃ = R₂×R₄. No current flows through galvanometer.
