MCQ
An alternating current is given by $I=I_{A} \sin \omega t+I_{B} \cos \omega t$. The r.m.s. current will be :-
  • A
    $\sqrt{I_{A}^{2}+I_{B}^{2}}$
  • B
    $\frac{\sqrt{I_{A}^{2}+I_{B}^{2}}}{2}$
  • $\sqrt{\frac{\mathrm{I}_{\mathrm{A}}^{2}+\mathrm{I}_{\mathrm{B}}^{2}}{2}}$
  • D
    $\frac{\left|I_{A}+I_{B}\right|}{\sqrt{2}}$

Answer

Correct option: C.
$\sqrt{\frac{\mathrm{I}_{\mathrm{A}}^{2}+\mathrm{I}_{\mathrm{B}}^{2}}{2}}$
(C)
Sol. $i_{\text {rms }}=\sqrt{\frac{\int I^{2} d t}{\int d t}}$
$\sqrt{\frac{I_{A}^{2}+I_{B}^{2}}{2}}=i_{\text {rms }}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

The focal lengths for violet, green and red light rays are ${f_V},{f_G}$ and ${f_R}$ respectively. Which of the following is the true relationship
In a series resonant $LCR$ circuit, the voltage across $R$ is $100\,volts$ and $R = 1\, k\Omega $ with $C = 2\,\mu f$ .The resonant frequency $\omega $ is $200\,rad/s$. At resonance the voltage across $L$ is
The refractive index of water is $4 / 3$ and that of glass is $5/3$. What will be the critical angle for the ray of light entering water from the glass
What will be the minimum angle of incidence such that the total internal reflection takes place from both the surface?.......$^o$
There are $50$ $turns$ of a wire in every $cm$ length of a long solenoid. If $4\, ampere$ current is flowing in the solenoid, the approximate value of magnetic field along its axis at an internal point and at one end will be respectively
Following figure shows two processes $A$ and $B$ for a gas. If $\Delta Q_A$ and $\Delta Q_B$ are the amount of heat absorbed by the system in two cases, and $\Delta U_A$ and $\Delta U_B$ are changes in internal energies, respectively, then
Two men are carrying a uniform bar of length $L$, on their shoulders. The bar is held horizontally such that younger man gets $(1/4)^{th}$ load. Suppose the younger man is at the end of the bar, what is the distance of the other man from the end
With rise in temperature, the Young's modulus of elasticity
Two particles of mass $m$ are constrained to move along two horizontal frictionless rails that make an angle $2\theta $ with respect to each other. They are connected by a spring with spring constant $k$ . The angular frequency of small oscillations for the motion where the two masses always stay parallel to each other (that is the distance between the meeting point of the rails and each particle is equal) is 
A person with his hand in his pocket is skating on ice at the rate of $10 m / s$ and describes a circle of radius $50 m$. What is his inclination to vertical: $\left( g =10 m / sec ^2\right)$