Question

The frequency of voltage for an AC circuit, the equation of alternating voltage is \[V = 200\sin 314t\] is?
A. 50Hz
B. 55Hz
C. 60Hz
D. 65Hz

Answer 1

Hint We will derive the equation of alternating voltage then we will compare it with the given equation and will find the value of angular frequency. After getting angular frequency we will get the frequency by using the formula \[\omega = 2\pi f\] .

Complete step-by-step solution
Alternating Voltage is that voltage whose magnitude changes with time and its direction is reversed periodically.
 \[e = - \dfrac{{d\phi }}{{dt}}\] , where \[\phi \] = flux by magnetic field
                                 e = instantaneous voltage
 \[e = - \dfrac{{d(\overrightarrow B .\overrightarrow A )}}{{dt}}\] , B= magnetic field and A= area
 \[e = - \dfrac{{d(BA\cos \theta )}}{{dt}}\] , \[\omega = \dfrac{\theta }{t}\]
 \[e = - BA\dfrac{{d(\cos (\omega t))}}{{dt}}\] , \[e = BA\omega \sin (\omega t)\]
 \[e = {e_ \circ }\sin (\omega t)\] , \[{e_ \circ }\] = peak voltage
Now compare this equation with \[V = 200\sin 314t\]
 \[\omega = 314{s^{ - 1}}\]
 \[\omega = \dfrac{{2\pi }}{T}\] , T= time period
 \[\omega = 2\pi f\] , f= frequency of the voltage
 \[f = \dfrac{\omega }{{2\pi }} = \dfrac{{314}}{{2\pi }}\]
 \[f = 50Hz\]

Option(A) 50Hz

Additional information
Alternating voltage can be produced in two different ways
1)By rotating the coil inside the uniform magnetic field at constant speed
2)By rotating the magnetic field around the stationary coil at the constant speed.
The coil rotates between the magnetic field in small AC generators, while the magnetic field rotates around the coil in large ac generators due to certain economic considerations.

Note While comparing the equation, look carefully whether the equation is in sin or cos, if it’s in cos and the 90 degree to convert it into sin. Alternating voltage graph is sinusoidal, that's why the equation has a sin component.
Power supplies to hoses are AC instead of DC. Many countries have the supply of either 50Hz or 60Hz. Some countries like Japan have a mixture of both these frequencies.