Question 420: AC fundamentals

Question

The instantaneous value of an alternating current is given by $$\mathrm{i}=50 \sin (100 \pi \mathrm{t})$$. It will achieve a value of $$25 \mathrm{~A}$$ after a time interval of $$\left(\sin 30^{\circ}=0.5\right)$$

Accepted Answer

Given the instantaneous value of an alternating current as $$\mathrm{i}=50 \sin (100 \pi \mathrm{t})$$, and we're asked to find at what time interval it achieves a value of $$25 \mathrm{A}$$. Using the given information ($$\sin 30^{\circ}=0.5$$), we set up the equation:
$$25 = 50 \sin(100 \pi t)$$
To find the value of $$t$$, we divide both sides by 50:
$$\frac{25}{50} = \sin(100 \pi t)$$
$$0.5 = \sin(100 \pi t)$$
Given $$\sin 30^{\circ}=0.5$$, we have:
$$\sin(100 \pi t) = \sin 30^{\circ}$$
Therefore,
$$100 \pi t = 30^{\circ}$$
To convert degrees into radians (since we're dealing with radians in the sine function), remember that $$180^{\circ} = \pi$$ radians. Thus, $$30^{\circ}$$ is $$\frac{\pi}{6}$$ radians:
$$100 \pi t = \frac{\pi}{6}$$
Cancelling $$\pi$$ from both sides and solving for $$t$$ yields:
$$100t = \frac{1}{6}$$
$$t = \frac{1}{600} \mathrm{~S}$$
Therefore, the correct answer is:
Option D: $$\frac{1}{600} \mathrm{~S}$$

Answer

$$\frac{1}{300} \mathrm{~S}$$

Answer

$$\frac{1}{100} \mathrm{~S}$$

Answer

$$\frac{1}{200} \mathrm{~S}$$

Answer

$$\frac{1}{600} \mathrm{~S}$$

AC fundamentals

The instantaneous value of an alternating current is given by $\mathrm{i}=50 \sin (100 \pi \mathrm{t}). It will achieve a value of 25 \mathrm{~A} after a time interval of \left(\sin 30^{\circ}=0.5\right)

Choose the correct answer: