The current I in an a.c circuit is given by the equation I = 30sin100πt

Question

The current, I in an a.c circuit is given by the equation I = 30sin100πt, where t is the time in seconds. Deduce the following from this equation.

a) Frequency of the current

b) Peak value of the current

c) Root mean square value of the current

Solution

We can compare the equation I = I₀Sin2πft with I = 30sin100πt

a) To find the frequency of the current and from the above comparison, we can see that:

2πft = 100πt

And by dividing both sides by 2πt, we will now have:

f = 100πt/2πt = 50Hz

Thus, the frequency of the current is 50 Heartz.

b) By applying the same comparison method, we can see that peak current is:

I₀ = 30A

Thus, the peak current is 30 Ampere.

C) The root mean square (r.m.s or rms) value of the current is:

I_rms = I₀ / √2 = 30/√2 = 21.21A

Therefore, the root mean square value of the current is 21.21 Ampere.