(a) Define r.m.s. value of AC.<br>The variation with time t of the sinusoidal current I in a resistor of resistance 450Ω is shown in figure.<br>Use data from the Figure to determine, for the time t = 0 to t =30ms. <br> (b) The Frequency of the current.<br> (c) The mean current. <br> (d) The root-mean-square current. <br> (e) The energy dissipated by the resistor. <br>

Solution:

(a)
RMS value of AC current is that steady current which when passed through a resistance for a given time produces the same amount of heat as the alternating current does in the same resistance in the same time.

The period of a wave is the time for a particle on a medium to make one complete vibrational cycle.

Thus, Period in above graph is 15.

(b) Frequency is Given as f=$\frac{1}{Period}$=$\frac{1}{15}$=0.067.

(c) The value of mean current for A.C current is zero. This is because the mean current represents the average value over a complete cycle, and the average value becomes zero in above graph.

(d) From Graph,

Peak Value of Current (I₀) = 0.75

We know, I_rms=$\frac{{{I_0}}}{{\sqrt 2 }}$ = $\frac{{0.75}}{{\sqrt 2 }}$ = 0.53

(e) Given:

R = 450Ω

Time (t) = 30ms = 30 × 10^-3

We Know,

Energy Dissipated = E = I_rms² × R × T

= 0.53² × 450 × 30 × 10^-3

= 3.79J