Question

A magnetic circuit with a relative permeability of 50 has a core cross section of $5c{m}^2$ and mean core length of 25 cm. The coil on the core has 120 turns with an mmf of 500 AT. The magnetic core flux is

• A. 0.75 mWb
• B. 0.06 mWb
• C. 0.25 mWb
• D. 1 mWb

Answer 1

The correct option is B 0.06 mWb

$\text{Given,}$
${\mu }_r=50$
${\mu }_0=4\pi \times {10}^{-7}$

$\text{We know that,}\mu ={\mu }_0{\mu }_r$

$\text{Cross-section area,}A=5c{m}^2=5\times {10}^{-4}{m}^2$

$\text{Core length,}l=25cm=25\times {10}^{-2}m$

$\text{Now, Reluctance}=\frac{l}{{\mu }_0{\mu }_{r}A}$$=\frac{25\times {10}^{-2}}{4\pi \times {10}^{-7}\times 50\times 5\times {10}^{-4}}$

$\text{Also, Flux}=\frac{\text{mmf}}{\text{Reluctance}}$

$=\frac{500\times 4\pi \times {10}^{-7}\times 50\times 5\times {10}^{-4}}{25\times {10}^{-2}}$

$=0.628\times {10}^{-4}Wb=0.0628mWb\simeq 0.06mWb$