Question

3. An alternating current, i is represented by i=10sin942t Amperes. (a) Determine, (i) The frequency, f(6 Marks) (ii) The period, T (4 Marks) (b) Sketch the waveform/corresponding current versus time graph and label the important values ( 7 Marks)

Answer 1

The frequency of the alternating current is approximately 150 Hz, and the period is approximately 0.00667 seconds. The waveform of the current versus time graph is a sinusoidal wave with a period of 0.00667 seconds and an amplitude of 10A.

Step-by-step explanation:

The equation for the alternating current is given as i(t) = Io sin (wt - θ). To determine the frequency (f) of the current, we need to find the value of w. From the given equation i(t) = 10sin942t, we can see that w = 942. The frequency is equal to the angular frequency divided by 2π, so f = w / 2π = 942 / (2π) ≈ 150 Hz.

The period (T) of the current is the reciprocal of the frequency, so T = 1 / f ≈ 1 / 150 ≈ 0.00667 seconds.

To sketch the waveform of the current versus time graph, we can plot the values of the current at different time intervals. For example, at t = 0, the current is 0, and at t = 0.00667, the current is 10A. The graph will be a sinusoidal wave with a period of 0.00667 seconds and an amplitude of 10A.

Answer 2

The frequency of the alternating current is approximately 150 Hz, and the period is approximately 0.00667 seconds.

The waveform of the current versus time graph is a sinusoidal wave with a period of 0.00667 seconds and an amplitude of 10A.

The equation for the alternating current is given as i(t) = Io sin (wt - θ).

The frequency (f) of the current, we need to find the value of w.

From the given equation i(t) = 10sin942t,

w = 942.

The frequency is equal to the angular frequency divided by 2π,

f = w / 2π

f = 942 / (2π)

f ≈ 150 Hz.

The period (T) of the current is the reciprocal of the frequency,

T = 1 / f

T ≈ 1 / 150

T ≈ 0.00667 seconds.

To sketch the waveform of the current versus time graph, we can plot the values of the current at different time intervals. For example, at t = 0, the current is 0, and at t = 0.00667, the current is 10A. The graph will be a sinusoidal wave with a period of 0.00667 seconds and an amplitude of 10A.