Question

An alternating emf is represented as V = 10
sin 314t. The instantaneous emf at t = =
(1) 10V
(2) 4 V
(3) 5 V
(4) 6 V
600 S is​

Answer 1

Explanation:

Given An alternating emf is represented as V = 10  sin 314 t and frequency 50 hz. The instantaneous emf at t = 1/600 sec is

• Given Vo = 10 V, f = 50 hz
• We know that ω = 2 π f
•                            = 2 x π x 50
•                             = 100 π
• Given V = 10 sin 100π t
• Now V at t = 1/600 s = 10 sin (100π x 1/600)
•                                   = 10 sin π / 6
•                                     = 10 sin 30
•                                     = 10 x 1/2  
•                                     = 5 Volts

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Answer 2

An alternating emf can be represented by the equation

V(t) = $V_{0}$ sin ωt

where ω = 2$\pi$f

f being the frequency

Here you can see in the give equation that ω = 314

314 = 2 x $\pi$ x f

f = 50 Hz

So for t = $\frac{1}{600}$

V($\frac{1}{600}$) = 10 sin 2x$\pi$x50x$\frac{1}{600}$

V($\frac{1}{600}$) = 10 sin 100x$\pi$x$\frac{1}{600}$

V($\frac{1}{600}$) = 10 sin $\frac{\pi}{6}$

since sin $\frac{\pi}{6}$  = sin 30 = $\frac{1}{2}$

V($\frac{1}{600}$) = 10 x ($\frac{1}{2}$) = 5V