D4.8) In the magnetic circuit of Example 4.4, an air gap of length 0.5 mm is cut in the lower leg of the core. Find the self-inductances and mutual inductance of the two coils. EXAMPLE 4.4=The magnetic circuit shown in Fig. 4.7 has the following dimensions: Ac12 cm² and le = 50 cm. The magnetic core has a relative permeability ₁ =20,000. The first coil has N₁ = 500 turns and the second has N₂ = 1000 turns. "111N₁N₂FIGURE 4.7 Mutual inductance.12v2

Given data are: The cross-sectional area of the core, Ac=12 cm2=12×10-4m2 Length of the core,…

Answered: In the magnetic circuit of Example 4.4,…

Introductory Circuit Analysis (13th Edition)

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Author:Robert L. Boylestad

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D4.8) In the magnetic circuit of Example 4.4, an air gap of length 0.5 mm is cut in the lower leg of the core. Find the self-inductances and mutual inductance of the two coils.

EXAMPLE 4.4
=
The magnetic circuit shown in Fig. 4.7 has the following dimensions: Ac
12 cm² and le = 50 cm. The magnetic core has a relative permeability ₁ =
20,000. The first coil has N₁ = 500 turns and the second has N₂ = 1000 turns.

"1
11
N₁
N₂
FIGURE 4.7 Mutual inductance.
12
v2

Expert Solution

Step 1

Given data are:

The cross-sectional area of the core, A_c=12 cm²= $12 \times 10^{- 4} m^{2}$
Length of the core, l_c=50cm=0.5m
Relative permeability of the magnetic core, $μ_{r} = 20, 000$
The number of turns on the primary side, N₁=500 turns
The number of turns on the secondary side, N₂=1000 turns
Length of the air gap,l_g=0.5mm= $0.5 \times 10^{- 3} m$
$Permeability of free space, μ_{o} = 4 π \times 10^{- 7} \frac{H}{m}$

The above figure 4.7 after air gap can be drawn as:

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