Question

In a two winding transformer with a laminated core, the winding with $N_1=200$ turns is connected to a voltage to produce a flux density in the core B = 1.2 sin 377t. The second winding with $N_2=400$ turns, is left open circuited. The stacking factor of the core is 0.95 i.e., the core occupies 95% of the gross core volume. The gross cross sectional area of the core is 25 cm${}^2$ and ${\mu }_r$ for the core is 10000. The core length $l_c=90cm$. The rms value of the applied voltage is ___________V.

(Neglect primary impedance)

• A. 151.95

Answer 1

The correct option is A 151.95
$\text{Flux,}\varphi =BA\times 0.95$

$=1.2\times 25\times ({10}^{-2}{)}^2\times 0.95\times sin377t$

$\varphi =2.85\times {10}^{-3}sin377t$

$emf=N_1\frac{d\varphi }{dt}=200\times \frac{d}{dt}(2.85\times {10}^{-3}sin377t)$

$=200\times 2.85\times {10}^{-3}\times 377\times cos377tV$

$\text{e = 214.89 cos 377 t}$

$\text{Rms value of applied voltage}=\frac{214.89}{\sqrt{2}}=151.95\text{V}$