## Kirchhoff's Voltage Law (KVL) / Mesh Analysis

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

## 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.

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

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

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