Question

. The equation for an alternating current is given by i = 77 sin 314t. Find the peak
value, frequency, time period and instantaneous value at t = 2 ms,

Answer 1

Given:

The equation for an alternating current is given by i = 77 sin 314t.

To find:

• Peak value
• Time period
• Frequency
• value at t = 2 sec

Calculation:

Equation of AC :

$\therefore \: i = 77 \sin(314t)$

Now, for peak value , sin(314t) value should be max and equal to 1 :

$\implies\: i_{max} = 77 \times 1$

$\implies\: i_{max} = 77 \: amp$

Now, time period:

$\therefore \: t = \dfrac{2\pi}{ \omega}$

$\implies \: t = \dfrac{2\pi}{314}$

$\implies \: t = \dfrac{2 \times 3.14}{314}$

$\implies \: t = \dfrac{2 \times 314}{314 \times 100}$

$\implies \: t = 0.02 \: sec$

Now, frequency:

$\therefore \: f = \dfrac{1}{t} = \dfrac{1}{0.02} = 50 \: hz$

Now, value:

$\therefore \: i = 77 \sin(314t)$

$\implies \: i = 77 \sin(314 \times 2 \times {10}^{ - 3} )$

$\implies \: i = 77 \sin(3.14 \times 2 \times {10}^{ - 1} )$

$\implies \: i = 77 \sin(0.2\pi)$

$\implies \: i = 77 \times 0.58$

$\implies \: i = 45.25 \: amp$

Hope It Helps.