In the diagram, two sinusoidal voltages of the same frequency are shown. What is the frequency and the phase relationship between the voltages?
      

An ideal inductor connected to a cell is shown in figure. Select the correct relations between readings of ammeters $A_1 and A_2$ just after the switch is closed and a long time after closing the switch

$1. A_1>A_2 ; A_1<A_2$
$2. A_1>A_{2 }; A_2=A_1$
$3. A_1<A_2 ; A_1 < A_2$
$4. A_1<A_2 ; A_1 =A_2$

A direct current of \(2~\text{A}\) and an alternating current having peak value \(2~\text{A}\) flow through two identical resistance at the same time. The ratio of heat produced in the two resistance will be:
1. \(1:1\)
2. \(1:2\)
3. \(2:1\)
4. \(4:1\)

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. \( 5 A \sin \left(\omega t+30^{\circ}\right)\)

Given below are two statements: 

When 100 volt d.c. is applied across a solenoid, a current of 1.0 A flows in it. When 100 volt a.c. is appliead across the same coil, the current drops to 0.5 A. If the frequency of a.c. source is 50 Hz the impedance and inductance of the solenoid is

1. 200 $\mathrm{\Omega }$ and 0.55 H

2. 100 $\mathrm{\Omega }$ and 0.86 H

3. 200 $\mathrm{\Omega }$ and 1.0 H

4. 100 $\mathrm{\Omega }$ and 0.93 H

The line that draws power supply to your house from the street has 

(a) zero average current
(b) 220 V average voltage
(c) voltage and current out of phase by $90°$
(d) voltage and current possibly differing in phase $\mathrm{\varphi } \mathrm{such} \mathrm{that} \left|\mathrm{\varphi }\right|<\frac{\mathrm{\pi }}{2}$

1. (b, c)

2. (a, d)

3. (b, d)

4. (a, c)