The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability {4 \over 3} for this wavelength, will be :

A vessel of depth 2h is half filled with a liquid of refractive index $$2\sqrt{2}$$ and the upper half with another liquid of refractive index $$\sqrt{2}$$ . The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

The aperture diameter of a telescope is 5m. The separation between the moon and the earth is 4 × 105 km. With light of wavelength of 5500 $$\stackrel{o}{A}$$, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to :

There is a small source of light at some depth below the surface of water (refractive index = {4 \over 3}) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly) : [Use the fact that surface area of a spherical cap of height h and radius of curvature r is 2$$\pi$$rh]:

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the mirror (x) is correctly given by : (Graphs are drawn schematically and are not to scale)

A potentiometer wire PQ of 1 m length is connected to a standard cell E1. Another cell E2 of emf 1.02 V is connected with a resistance ‘r’ and switch S (as shown in figure). With switch S open, the null position is obtained at a distance of 49 cm from Q. The potential gradient in the potentiometer wire is :

Model a torch battery of length $$l$$ to be made up of a thin cylindrical bar of radius ‘a’ and a concentric thin cylindrical shell of radius ‘b’ filled in between with an electrolyte of resistivity $$\rho$$ (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for :

Two resistors 400$$\Omega$$ and 800$$\Omega$$ are connected in series across a 6 V battery. The potential difference measured by a voltmeter of 10 k$$\Omega$$ across 400 $$\Omega$$ resistor is close to :

The value of current i1 flowing from A to C in the circuit diagram is :

An electrical power line, having a total resistance of 2 $$\Omega$$, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately :

A galvanometer of resistance G is converted into a voltmeter of range 0 – 1 V by connecting a resistance R1 in series with it. The additional resistance that should be connected in series with R1 to increase the range of the voltmeter to 0 – 2 V will be :

In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point B with respect to the point A is :

A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of 6 mA it produces a deflection of 2o, its figure of merit is close to :

A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit :

In the figure shown, the current in the 10 V battery is close to :

A battery of 3.0 V is connected to a resistor dissipating 0.5 W of power. If the terminal voltage of the battery is 2.5 V, the power dissipated within the internal resistance is :

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity $$\rho$$C, $$\rho$$T, $$\rho$$M and $$\rho$$A respectively. Then :

The current I1 (in A) flowing through 1 $$\Omega$$ resistor in the following circuit is :

In a building there are 15 bulbs of 45 W, 15 bulbs of 100 W, 15 small fans of 10 W and 2 heaters of 1 kW. The voltage of electric main is 220 V. The minimum fuse capacity (rated value) of the building will be :

The length of a potentiometer wire is 1200 cm and it carries a current of 60 mA. For a cell of emf 5V and internal resistance of 20$$\Omega$$, the null point on it is found to be a 1000 cm. The resistance of whole wire is :