Question

The alternating current, in a given set up, varies with time in the manner shown. The rms value of this current, over one cycle, is

(1) 3 A

(2) 3.17 A

(3) 3.28 A

(4) 3.62 A

Answer 1

(2) 3.17 A

The rms value, by definition, is obtained by taking the average of the squares of all values (over one complete cycle) and then taking the square root of this average. 

For the given case, we have 

For (t = 0) to (t = 1); sum of the squares of all values = (2)³ = 4 

For (t = 1) to (t = 3); sum of the squares of all values = (-4)² x 2 = 32 

For (t = 3) to (t = 4); sum of the squares of all values = (2)² x 1 = 4 

∴ Sum of the squares of all values over one complete cycle (= 4s) = (4 + 32 + 4)A² = 40 A²

∴ Average of the squared values = (40/4)A² = 10A²

∴ rms value = √10 A

= 3.17 A