Average and RMS Value of Alternating Current and Voltage

The instantaneous current and voltage of an AC circuit are given by $\mathrm{i}=10\sin \left(314\mathrm{t}\right) \mathrm{A}$ and $\mathrm{V}=100\sin \left(314\mathrm{t}\right) \mathrm{V}$. The power dissipation in the circuit is

The RMS value of voltage of the waveform shown below is, $v_{rms}=\frac{k}{\sqrt{3}} \mathrm{V}$, find the value of $k$.

An alternating voltage $E=200\sqrt{2}\sin \left(100\mathrm{t}\right)$ is connected to a $1$ micro farad capacitor through an AC ammeter. The reading of the ammeter shall be:

If a capacitor of $8\mathrm{ }\mathrm{\mu F}$ is connected to a $220\mathrm{ }\mathrm{V},\mathrm{ }100 \mathrm{H}\mathrm{z}$, AC source and the current passing through it is $65 \mathrm{m}\mathrm{A}$ then the rms voltage across it is

The form factor is the ratio of 

Find the form factor of the wave form given in figure-

Form factor of a sawtooth waveform with a period of $3 \sec$ and a peak voltage of $150 \mathrm{V}$ is-

The $\mathrm{rms}$ value of sinusoidally varying current is_____. That of its average value.

The form factor of the sinusoidal waveform is ?

A wire is carrying a direct current of $20\mathrm{A}$ and a sinusoidal alternating current of peak value $20\mathrm{A}$. Find the $\mathrm{rms}$ value of the resulting current

An AC voltage (in Volt) varies with time $\mathrm{t}$ (in seconds) as $\mathrm{V}=100 \sin \left(50\mathrm{\pi t}\right)$.

The peak value of voltage, the $\mathrm{rms}$ value of the voltage and the frequency respectively are

In an ac generator, the no. of turns in the coil is $2000$ and the area of the coil is $0.1 {\mathrm{m}}^2$. The coil is rotating at an angular frequency of $200 \raisebox{1ex}{$\mathrm{rad}$}\!\left/ \!\raisebox{-1ex}{$\sec $}\right.$ in a magnetic field of $0.2 \mathrm{T}$, what is the peak value of the induced emf?

The peak factor of the sinusoidal wave form is?

The value from positive to negative peak of the sine wave si called?

The r-m-s value of AC voltage$V$ in terms of $\sin x$ and $\cos x$ is always same for a complete cycle.

The r-m-s value of $V_1=V_p \sin \left(\omega t\right)$ and $V_2=V_p \cos \left(\omega t\right)$ is _____ times $V_p$ for a complete cycle. Here, $V_p$ is peak voltage.

Compare the r-m-s value of $V_1=V_p \sin \left(\omega t\right)$ and $V_2=V_p \cos \left(\omega t\right)$ for a complete cycle. Here, $V_p$ is peak voltage.

The voltage supplied to a circuit is given by $\mathrm{V}={\mathrm{V}}_2{\mathrm{t}}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ where $\mathrm{t}$ is in sec. The $\mathrm{rms}$ value of voltage for period $\mathrm{t}=0$ to $\mathrm{t}=1 \sec$ is 

AC voltage supplied to resistor of resistance $10\mathrm{\Omega }$ is $\mathrm{E}=20 \sin \left(300\mathrm{t}-\frac{\mathrm{\pi }}{4}\right)$. The $\mathrm{rms}$ value of current is 

If the peak value of current in $50 \mathrm{Hz}$ a.c. supply is $10\mathrm{A}$ then the average value of alternating current for time-interval $0 \mathrm{to} \raisebox{1ex}{$\mathrm{T}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ is _____?