AC Voltage Applied to a Resistor

A $15.0$ $\text{μF}$  capacitor is connected to $220$ $\text{V,}$ $50$ $\text{Hz}$ source. The capacitive reactance and the RMS current would be:

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

A resistor of  $200\Omega$  and a capacitor of 15.0 $\text{μF}$  are connected in series to a 220 V, 50 Hz a.c. source. Calculate

​(i) The current in the circuit.

(ii) The rms voltage across the resistor and the capacitor.

The instantaneous current and voltage of an a.c. circuit are given by $I=10\sin 300t \mathrm{A}$ and $V=200\sin 300t \mathrm{V}$. What is the power dissipation in the circuit?

If $E=500\sin \left(100\pi t\right)$ Volt, then the time taken to reach the maximum point from zero.

The average value of current $i=I_{\mathrm{m}}\sin \omega t$ from $t=\frac{\pi }{2\omega }$ to $t=\frac{3\pi }{2\omega }$ is how many times of $I_{\mathrm{m}}$?

Find the value of rms current if, the current function is given by $I=I_1\cos \omega t+I_2\sin \omega t.$

What will be the root mean square value of current? When a direct current of $5 \mathrm{A}$ is superimposed on an alternating current $I = 10 \sin \omega t \mathrm{A}$.

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

Assertion : The alternating current lags behind the e.m.f. by a phase angle of $\frac{\pi }{2}$, when AC flows through an inductor.
Reason : The inductive reactance increases as the frequency of AC source decreases.

Assertion: In a purely resistive ac circuit instantaneous power varies sinusoidally.

Reason: Applied ac voltage varies sinusoidally.

A sinusoidal voltage $v=200\sin 314t$ is applied to a resistor of $10\Omega$ resistance. Calculate the power dissipated as heat in $\mathrm{watt}$.

A sinusoidal voltage $v=200\sin 314t$ is applied to a resistor of $10 \Omega$ resistance. Calculate the rms value of the current.

A sinusoidal voltage $v=200\sin 314t$ is applied to a resistor of $10\Omega$ resistance. Calculate the rms value of the voltage.

A sinusoidal voltage $v=200\sin 314t$ is applied to a resistor of $10\Omega$ resistance. Calculate the frequency of the supply.

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.

The average value of $\cos x$ for the interval $\left[0,\frac{\mathrm{\pi }}{2}\right]$ is _____.

The ratio of average value of alternating voltage for the time interval $0$ to $\raisebox{1ex}{$\mathrm{T}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ and $0$ to $\raisebox{1ex}{$\mathrm{T}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ will be

Average value of current in a.c circuit containing resistor is for time-interval $0$ to $\frac{\mathrm{T}}{4}$