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When an ac source of e.m.f. e=E₀  sin(100 t) is connected across a circuit, the phase difference between the e.m.f. e and the current I in the circuit is observed to be /4, as shown in the diagram. If the circuit consists possibly only of RC or LC in series, find the relationship between the two elements
 

1. R = 1kΩ, C = 10 µF
2. R = 1kΩ, C = 1 µF
3. R = 1kΩ, L = 10H
4. R = 1kΩ, L = 1H

The r.m.s. value of potential difference V shown in the figure is
 

1. ${\mathrm{V}}_0/2$ 
2. ${\mathrm{V}}_0/\sqrt{3}$
3. ${\mathrm{V}}_0$
4. ${\mathrm{V}}_0/\sqrt{2}$

If the total charge stored in the LC circuit is Q₀, then for t $\ge$ 0
1. The charge on the capacitor is Q = Q₀ cos$\left(\frac{\mathrm{\pi }}{2}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\frac{\mathrm{t}}{\sqrt{\mathrm{LC}}}\right)$  
2. The charge on the capacitor is Q = Q₀ cos$\left(\frac{\mathrm{\pi }}{2}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>\frac{\mathrm{t}}{\sqrt{\mathrm{LC}}}\right)$
3. The charge on the capacitor is Q = -LC$\frac{{\mathrm{d}}^2\mathrm{Q}}{{\mathrm{dt}}^2}$
4. The charge on the capacitor is Q = $\frac{1}{\sqrt{\mathrm{LC}}}\frac{{\mathrm{d}}^2\mathrm{Q}}{{\mathrm{dt}}^2}$

Two coherent point sources S₁ and S₂ are separated by a small distance ‘d’ as shown. The fringes obtained on the screen will be

 
1. Points
2. Straight lines
3. Semi-circles
4. Concentric circles

In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on  for constructive interference at P between the ray BP and reflected ray OP

 
cos  = 3$\mathrm{\lambda }$/2d
cos  =  $\mathrm{\lambda }$/4d
sec  - cos  =  $\mathrm{\lambda }$/d
sec  - cos  =  4$\mathrm{\lambda }$/d

Speed of light is
1. The same in medium-1 and medium-2
2. Larger in medium-1 than in medium-2
3. Larger in medium-2 than in medium-1
4. Different at b and d

The phases of the light wave at c, d, e and f are ${\mathrm{\varphi }}_{\mathrm{c}}$, ${\mathrm{\varphi }}_{\mathrm{d}}$, ${\mathrm{\varphi }}_{\mathrm{e}}$ and ${\mathrm{\varphi }}_{\mathrm{f}}$ respectively. It is given that ${\mathrm{\varphi }}_{\mathrm{c}}<mspace\; width="1em"></mspace>\ne <mspace\; width="1em"></mspace>{\mathrm{\varphi }}_{\mathrm{f}}$
1. ${\mathrm{\varphi }}_{\mathrm{c}}$ cannot be equal to ${\mathrm{\varphi }}_{\mathrm{d}}$
2. ${\mathrm{\varphi }}_{\mathrm{d}}$ can be equal to ${\mathrm{\varphi }}_{\mathrm{e}}$
3. $({\mathrm{\varphi }}_{\mathrm{d}}-<mspace\; width="1em"></mspace>{\mathrm{\varphi }}_{\mathrm{f}})$ is equal to $({\mathrm{\varphi }}_{\mathrm{c}}-<mspace\; width="1em"></mspace>{\mathrm{\varphi }}_{\mathrm{e}})$
4. $({\mathrm{\varphi }}_{\mathrm{d}}-<mspace\; width="1em"></mspace>{\mathrm{\varphi }}_{\mathrm{c}})$ is not equal to $({\mathrm{\varphi }}_{\mathrm{f}}-<mspace\; width="1em"></mspace>{\mathrm{\varphi }}_{\mathrm{e}})$

In an AC circuit, V and l are given by
                        V = 100 sin(100t) volt
and                   l = 100 sin$\left(100<mspace\; width="1em"></mspace>\mathrm{t}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\frac{\mathrm{\pi }}{3}\right)$ amp
The power dissipated in the circuit is
1. 10${}^4$ W
2. 2.5 kW
3. 5 kW
4. 10 W

The average current in terms of ${\mathrm{l}}_0$ for the waveform as shown is

1. ${\mathrm{l}}_0$
2. $\frac{{\mathrm{l}}_{\mathrm{o}}}{3}$
3. $\frac{{\mathrm{l}}_0}{2}$
4. $\frac{{\mathrm{l}}_0}{4}$

The bandwidth in a series L-C-R circuit is
1. $\frac{\mathrm{LC}}{2\sqrt{{\mathrm{R}}^2{\mathrm{C}}^2+<mspace\; width="1em"></mspace>4\mathrm{LC}}}$
2. $\frac{2\mathrm{LC}}{\sqrt{{\mathrm{R}}^2{\mathrm{C}}^2+<mspace\; width="1em"></mspace>4\mathrm{LC}}}$
3. $\frac{\sqrt{{\mathrm{R}}^2{\mathrm{C}}^2+<mspace\; width="1em"></mspace>4\mathrm{LC}}}{\mathrm{LC}}$
4. zero

An L-C circuit contains 10 mH inductor and a 25 $\mathrm{\mu }$F capacitor. The ratio of the time periods for the energy to be completely magnetic, is
1. 0, 1.57, 4.71
2. 1.57, 3.14, 4.71
3. 1.57, 4.71, 7.85
4. None of these
 

At time t = 0, when the charge on the capacitor plates is q, switch S${}_1$ is opened and S${}_2$ is closed. The maximum charge the capacitor can hold, is q${}_0$. Choose the correct statement from the following.
1. $\mathrm{q}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{q}}_0<mspace\; width="1em"></mspace>\cos \left(\frac{\mathrm{t}}{\sqrt{\mathrm{LC}}}+\hspace{0.17em}\frac{\mathrm{\pi }}{2}\right)$
2. $\mathrm{q}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{q}}_0<mspace\; width="1em"></mspace>\cos \left(\frac{\mathrm{t}}{\sqrt{\mathrm{LC}}}-<mspace\; width="1em"></mspace>\frac{\mathrm{\pi }}{2}\right)$
3. $\mathrm{q}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>-\mathrm{LC}\frac{{\mathrm{d}}^2\mathrm{q}}{{\mathrm{dt}}^2}$
4. $\mathrm{q}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>-\frac{1}{\sqrt{\mathrm{LC}}}\frac{{\mathrm{d}}^2\mathrm{q}}{{\mathrm{dt}}^2}$

A plane electromagnetic wave propagating in the x-direction has a wavelength of 6.0 mm. The electric field is in the y-direction and its maximum magnitude is 33 Vm${}^{-1}$. The equation for the electric field as function of x and t is
1. 11 sin $\mathrm{\pi }$ (t - x/c)
2. 33 sin $\mathrm{\pi }$ x 10${}^{11}$(t - x/c)
3. 33 sin $\mathrm{\pi }$ (t - x/c)
4. 11 sin $\mathrm{\pi }$ x 10${}^{11}$(t - x/c)

A perfectly reflecting mirror has an area of 1 cm${}^2$. Light energy is allowed to fall on it for 1 h at the rate of 10 W cm${}^{-2}$. The force acting on the mirror is
1. 67 x 10${}^{-8}$ N
2. 2.3 x 10${}^{-4}$ N
3. 10${}^{-3}$ N
4. zero

A young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is
1. hyperbola
2. circle
3. straight line
4. parabola

In Young's double slit experiment, the intensity at a point is (1/4) of the maximum intensity. Angular position of this point is
1. ${\sin }^{-1}\left(\frac{\lambda }{d}\right)$
2. ${\sin }^{-1}\left(\frac{\lambda }{2d}\right)$
3. ${\sin }^{-1}\left(\frac{\lambda }{3d}\right)$
4. ${\sin }^{-1}\left(\frac{\lambda }{4d}\right)$

In a Young's double slit experiment, the intensity at a point where the path difference is $\frac{\mathrm{\lambda }}{6}$ ($\mathrm{\lambda }$ being the wavelength of the light used) is l. If ${\mathrm{l}}_0$ denotes the maximum intensity. $\mathrm{l}/{\mathrm{l}}_0$ is equal to
1. $\frac{1}{\sqrt{2}}$
2. $\frac{\sqrt{3}}{2}$
3. $\frac{1}{2}$
4. $\frac{3}{4}$

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double slit experiment, is
1. infinite
2. five
3. three
4. zero