Mesh Analysis

Solved Numericals on KVL, Mesh analysis, Superposition theorem and Thevenin’s Theorem

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Kirchhoff's Voltage Law (KVL) / Mesh Analysis

Q) Find the current flowing through 1 Ω resistance by using Kirchhoff’s voltage law / Mesh analysis.

Mesh Analysis

For Mesh 1

130-0.2I_1-0.2I_1+0.2I_2-110=0

-0.4I_1+0.2I_2=-20   \ldots\ldots (1) 

For Mesh 2

-I_2+110-0.2I_2+0.2I_1-0.2I_2=0

0.2I_1-1.4I_2=-110   \ldots\ldots (2) 

I_1 = 96.1538 A (clockwise)

I_2 = 92.3076 A (clockwise)

\therefore  current flowing through 1 Ω resistor is 92.3076 A.

Electromagnetism Solved problems

Electromagnetism solved problems

Magnetic circuit with an air gap

Q) An iron ring has its mean length of flux path as 60 cm and its cross-sectional area as 15 cm². If relative permeability is 500. Find the current required to be passed through a coil of 300 turns wound uniformly around it to produce a flux density of 1.2 T. What would be the flux density with the same current if the iron ring is replaced by an air core.

Given: l = 60 cm; a = 15 cm²; \mu_r = 500 ; N = 300; B=1.2 T. 

MMF(F) = \dfrac{Bl}{\mu_0 \mu_r}  

F = \dfrac{1.2 \times 60 \times 10^{-2}}{4\pi \times 10^{-7}\times 500}

F = 1145.9155 AT

If iron ring is replaced by air core.

MMF(F) = \dfrac{B_{air}l}{\mu_0 \mu_r}  

B_{air} = 2.4 \times 10^{-3} T