Question

The current through a particular circuit element is given by i(t)=10sin(200πt)A in which the angle is in radians. a. Sketch i(t) to scale versus time.

Answer 1

The problem involves sketching a sinusoidal function representing current as a function of time, indicated by i(t) = 10sin(200πt), where the amplitude is 10 A and the period is 0.01 s.

Step-by-step explanation:

The question concerns the current (i(t)) through a circuit element, which is modeled by the function i(t) = 10sin(200πt), where t represents time.

When dealing with such functions, it's important to identify key characteristics like the amplitude and angular frequency (ω). In this function, the amplitude (I0) is 10 A, meaning this is the maximum current.

The angular frequency is 200π rad/s, which indicates how rapidly the sinusoidal function oscillates.

The period of the function is given by T = 2π / ω, which in this case is T = 1/100 s or 0.01 s.

This information would be leveraged to carefully sketch a sinusoidal wave, marking significant points such as the period and the amplitude on the axes representing time (t) and current (i(t)), respectively.