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An electric current has both D.C. and A.C. components: the D.C. component is 8 A and the A.C. component is I=6 sin ω t A. The Iᵣₘₛ value of the resultant current is ______.

Asked in GUJCET 2014 · RMS and mean values

• (1) 8.05 A
• (2) 9.05 A
• (3) 11.58 A
• (4) 13.58 A

Step-by-step solution

Why the other options are wrong

• (1) No single slip produces 8.05 A, barely above the d.c. part alone. Sanity check: the a.c. part adds (6²)/2=18 A² to the mean square, lifting the r.m.s. value to √82=9.05 A.
• (3) No single slip produces 11.58 A. Adding the d.c. value to the a.c. r.m.s. value gives 8+4.24=12.24 A, and even that is wrong: r.m.s. values combine through their squares, √64+18=9.05 A.
• (4) No single slip produces 13.58 A. Sanity check: the current never exceeds 8+6=14 A and spends most of each cycle well below it; its r.m.s. value is √64+18=9.05 A.

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