Q. 95.0( 1 Vote )

# An alternating current is given byi = i1 cos ωt + i2 sin ωt.The rms current is given byA. B. C. D.

The rms value of current is given by

… (i), where

i = current = i1 cos ωt + i2 sin ωt …. (ii)(given), t = time, ω = angular frequency, T = time period.

Now, squaring on both sides of (ii), we get

i2 = i12cos2ωt + 2i1i2sinωtcosωt + i22sin2ωt … (iii)

=

ow, … (v), where ω = angular frequency, T = time period = 2π/ω

Therefore, (iv) becomes:

=> [since sin nπ = 0, cos 0 = cos 2nπ = 1]

Hence, rms value of current i is (Ans)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Alternating Current59 mins
Kirchoff's Law for VoltageFREE Class
Quiz | Drift Velocity & Thermal VelocityFREE Class
Drift Velocity & Thermal VelocityFREE Class
Know about Internal Resistance & EMF42 mins
Ohm's Law - Full Concept in one Go59 mins
Quick Revision of Current Electricity68 mins
Quiz | Wheatstone BridgeFREE Class
Questions based on Kirchoff's Law for Voltage67 mins
10 Good Problems on Current Electricity41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses