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 = 1.2sin 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 $25c{m}^2$ and ${\mu }_r$ for the core is 10000. The core length $l_c=90$ cm. The rms value of the applied voltage is________V. (Neglect primary impedance).

• A. 151.95

Answer 1

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

$=1.2\times 25\times ({10}^{-2}{)}^2\times 0.95\times \sin 377t$

$\varphi =2.85\sin 377tmWb$

$\text{emf =}{N}_1\frac{d\varphi }{dt}=200\frac{d}{dt}\left(2.85\sin 377t\right)\times {10}^{-3}$

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

$\text{Rms value of applied voltage,}$

$=\frac{214.89}{\sqrt{2}}=151.95V$