Representation of AC Current and Voltage By Rotating Vectors-Phasors

Given below are two statements:
Statement-I: In an ac circuit, the current through a capacitor leads the voltage across it.
Statement-II: In a.c. circuits containing pure capacitance only, the phase difference between the current and the voltage is $\pi$In the light of the above statements, choose the most appropriate answer from the options given below:
 

Given below are two statements:

Statement-I: In an ac circuit, the current through a capacitor leads the voltage across it.

Statement-II: In a.c. circuits containing pure capacitance only, the phase difference between the current and the voltage is $\mathrm{\pi }$

In the light of the above statements, choose the most appropriate answer from the options given below:

Select the correct phasor diagram of the circuit having only resistance.

Derive an expression for average or mean value of alternating current for half cycle.

An A.C source supply voltage, $E=200 \sin 314\mathrm{t}$ is applied to a pure resistance circuit containing resistance $200 \mathrm{\Omega }$. Calculate the peak value of current.

If in ac circuit there is no leading or lagging between supplied voltage and current then ac circuit is named as

In a certain circuit, $E=200 \cos (314 \mathrm{t})$ and $I=\sin (314 \mathrm{t}+\mathrm{\pi }/4)$. Their vector representation is

In a circuit made up of resistance $4 \mathrm{\Omega }$, and inductance $0.01 \mathrm{H}$, an alternating emf $200 \mathrm{V}$ at $50 \mathrm{Hz}$ is connected, then the phase difference between the current and the emf in the circuit is:

$200 \mathrm{\Omega }$ resistance and $1 \mathrm{H}$ inductance are connected in series with an $\mathrm{AC}$ circuit. The frequency of the source is $\frac{200}{2\pi } \mathrm{Hz}$. Then phase difference in between $\mathrm{V}$ and $\mathrm{I}$ will be :-

In a certain circuit $E=200\cos \left(314\right)t$ and $I=\sin \left(314\mathrm{t}+\frac{\pi }{4}\right)$, their vector representation is :-

Two sinusoidal voltages of the same frequency are shown in the diagram. What is the frequency, and the phase relationship between the voltages

Frequency in $Hz$ Phase lead of $N$ over $M$ in radians
 

Assertion: In series $RL$ AC circuit, voltage leads the current.

Reason: In series $RC$ AC circuit, current leads the voltage.

In an $\mathrm{A}.\mathrm{C}$. circuit, the resistance of $R \mathrm{\Omega }$ is connected in series with an inductance $L$. If the phase angle between voltage and current be $45°$, the value of inductive reactance will be: 

In series $\mathrm{LCR}$ circuit, the phase angle between supply voltage and current is

Voltage and current in an AC circuit are given by $V=5\sin \left(100 \pi t-\frac{\pi }{6}\right)$ and $I=4\sin \left(100\pi t+\frac{\pi }{6}\right)$

For the equation $\mathrm{y}\left(\mathrm{t}\right)=5\left(\mathrm{cm}\right)\left[\sin \left(3\mathrm{\pi t}\right)+\sqrt{3}\cos \left(3\mathrm{\pi t}\right)\right]$ where $\mathrm{t}$ is in seconds, find amplitude and time period.

In a series $\mathrm{LCR}$ circuit, the potential drop across $\mathrm{L},\mathrm{ }\mathrm{C}$ and $\mathrm{R}$ respectively are $40 \mathrm{V}$, $120 \mathrm{V}$ and $60 \mathrm{V}$. Then, the source voltage is

A coil of inductive reactance $1/\sqrt{\mathrm{3 }}\mathrm{\Omega }$ and resistance $\mathrm{1 }\mathrm{\Omega }$ is connected to a 200 V, 50 Hz AC supply. The time lag between maximum voltage and current is

If the input voltage $V_{\mathrm{i}}$ to the circuit below is given by $V_{\mathrm{i}}\left(t\right)=A\cos \left(2\pi ft\right)\text{,}$ the output voltage is given by $V_{\mathrm{o}}\left(t\right)=B\cos \left(2\pi ft+\varphi \right)$.

Which one of the following four graphs best depict the variation of $\varphi$ vs $f$?

In an A.C. circuit, the resistance $\left(R\right)$ is connected in series with an inductor of self-inductance $\left(L\right)$. If phase angle between voltage and current be ${45}^o$ , the value of inductive reactance $\left(X_L\right)$ will be equal to.....