Question

An alternating voltage is generated by rotating a coil in a normal magnetic field with $50Hz$ frequency. If $V_{rms}$ = 220 V, then the maximum flux passing through the coil is:

• A. $0.99Wb$
• B. $0.4Wb$
• C. $0.6Wb$
• D. $0.7Wb$

Answer 1

The correct option is A $0.99Wb$

Given,

$f=50Hz$

$V_{rms}=220=\frac{V_0}{\sqrt{2}}$

$V_0=220\sqrt{2}V$

Induced emf in the coil is rate of change of magnetic flux,

$V=-\frac{d\varphi }{dt}=V_{0}sin\left(2\pi ft\right)$

$\varphi =\int d\varphi =-\int V_{0}sin\left(2\pi ft\right)dt$

$\varphi =\frac{V_0}{\left(2\pi f\right)}cos\left(2\pi ft\right)$

The maximum flux passing through the coil is

${\varphi }_m=\frac{V_0}{2\pi f}=\frac{220\sqrt{2}}{2\times 3.14\times 50}$

${\varphi }_m=0.990Wb$

The option A, is correct.