A time-varying current is given by $l=5\sin \left(\omega t+\begin{array}{c}\pi \\ 6\end{array}\right)$ Its r.m.s. value is (symbols have usual meanings)

$1. 5\sqrt{5} A$
$2. 10 A$
$3. \frac{5}{\sqrt{2}} A$
$4. \frac{15}{\sqrt{2}}A$

An alternating voltage $V\sqrt{2}\sin \omega t$ at different frequencies is applied across a capacitor C as shown in the figure. Which of the following graphs between RMS current $(I)$$$ observed by an ammeter and angular frequency $\omega$ of voltage is correct?
          
1.              2. 
3.              4. 

It is found that the current through the LCR series circuit is at its maximum. If $V_r,V_c\mathrm{ a}nd{\mathrm{ V}}_L$ are potential differences across resistance, capacitor, and inductor respectively, then which of the following is correct?

In a series L-C-R circuit, different physical quantities vary with frequency $\omega$. Which of the following curves represent the correct frequency variation of the corresponding quantity?

1. Curve (l) for R

2. Curve (ll) for $X_C$

3. Curve (lll) for $X_L$

4. All of these

For the circuit shown in figure below, the ammeter $A_2$ reads 1.6 A and ammeter $A_3$ read 0.4 A If ${\omega }_0$ is angular frequency and $f$ is frequency of ac, then

$1. {\omega }_0=\frac{4}{\sqrt{LC}}$
$2. f=\frac{2\pi }{\sqrt{LC}}$
$3. The ammeter A_1 reads 1.2 A$
$4. The ammeter A_1 reads 2 A$

If the reading of $V_1$ and $V_3$ are 100 V each, the reading of $V_2$ is

1. 0 V

2. 100 V

3. 200 V

4. Cannot be determined by given information

If current \(i_1=3A sin \omega t\) and current \(i_2=4A cos \omega t,\) then \(i_3\) is:

     

1. \(5 A \sin \left(\omega t+53^{\circ}\right) \)
2. \(5 A \sin \left(\omega t+37^{\circ}\right) \)
3. \(5 A \sin \left(\omega t+45^{\circ}\right) \)
4. \( 5 A \sin \left(\omega t+30^{\circ}\right)\)

A capacitor of capacitance 1 $\mu F$ is charged to a potential of 1 V. It is connected in parallel to an inductor of inductance ${10}^{-3}$H. What is the value of the maximum current that will flow in the circuit?

$1.$ $\sqrt{1000}$ $mA$
$2.$ $1$ $mA$ $$
$3.$ $1$ $\mu F$
$4.$ $1000$ $mA$

In a box Z of unknown elements (L or R or any other combination), an ac voltage $E=E_0\sin (\omega t+\varphi )$ $$is applied and the current in the circuit is found to be $I=I_0\sin (\omega t+\varphi +\frac{\pi }{4})$. The unknown elements in the box could be:

In the transformer shown in the figure, the ratio of the number of turns of primary to the secondary is $\frac{N_1}{N_2}=\frac{1}{50}$. If a battery of emf 10 V is connected across primary, then induced current through the load of 10 k$\Omega$ in the secondary is

$1. \frac{1}{20}A$
$2. Zero$
$3. \frac{1}{10}A$
$4. \frac{1}{5}A$