Question

A sinusoidal voltage has a value of 100 V at 2.5 ms and it takes time of 20 ms to complete one

cycle. Find the maximum value and time to reach it for the first time after zero.​

Answer 1

Given:

A sinusoidal voltage has a value of 100 V at 2.5 ms and it takes time of 20 ms to complete one cycle.

To find:

Max value and time taken to reach zero for 1st time?

Calculation:

Let max value be V :

$\therefore \: V2 = V \sin( \omega t)$

$\implies \: V2 = V \sin( \dfrac{2\pi}{T} \times t)$

$\implies \: 100= V \sin( \dfrac{2\pi}{20} \times 2.5)$

$\implies \: 100= V \sin( \dfrac{2\pi}{8} )$

$\implies \: 100= V \sin( \dfrac{\pi}{4} )$

$\implies \: 100= V \times \dfrac{1}{ \sqrt{2} }$

$\implies V = 100 \sqrt{2} \: volts$

So, max value is 100√2 volts.

So, time period (as per question) is 20 ms.

Now, since it's a sinusoidal wave, it will take half of time period to come to zero for 1st time.

So, required time = 20/2 = 10 ms.