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In the given circuit diagram, E = 5 V, r = 1 Ω, R₂ = 4 Ω, R₁ = R₃ = 1 Ω and C = 3 μF. Then, what will be the numerical value of charge on each plate of the capacitor?

A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between the plates is d. The space between the plates is now filled with two dielectrics: one has dielectric constant K₁ = 3 and thickness d/3, while the other has dielectric constant K₂ = 6 and thickness 2d/3. Capacitance of the capacitor is now

The resistance of a wire at 20°C is 20 Ω and at 500°C is 60 Ω. At which temperature will its resistance be 25 Ω?

In the circuit shown, the heat produced in the 5 Ω resistor is 10 cal s⁻¹. The heat produced per second in the 4 Ω resistor will be

A conducting circular loop is placed in a uniform magnetic field B = 0.025 T, with its plane perpendicular to the field. The radius of the loop is made to shrink at a constant rate of 1 mm s⁻¹. The induced emf when the radius is 2 cm is

Two metal plates having a potential difference of 800 V are 2 cm apart. It is found that a particle of mass 1.96 × 10⁻¹⁵ kg remains suspended in the region between the plates. The charge on the particle must be (e = 1.6 × 10⁻¹⁹ C)

Three charges are placed at the three vertices of an equilateral triangle of side a as shown in the figure. The force experienced by the charge placed at the vertex A in a direction normal to BC is

Two blocks A and B are placed one over the other on a smooth horizontal surface. The maximum horizontal force that can be applied on the lower block A, so that A and B move without separation, is 49 N. The coefficient of friction between A and B is

A block A of mass 100 kg rests on another block B of mass 200 kg and is tied to a wall as shown in the figure. The coefficient of friction between A and B is 0.2 and that between B and the ground is 0.3. The minimum force required to move the block B is (g = 10 m s⁻²)

A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a satellite orbiting a few 100 km above the earth's surface will approximately be (R = 6400 km)

A particle moving along x-axis has acceleration f at time t given by f = f₀(1 − t/T), where f₀ and T are constants. If the particle is at rest at t = 0, then the particle's velocity when f = 0 is

A balloon is filled at 27°C and pressure 1 atm by 500 m³ of He. At -3°C and pressure 0.5 atm, the volume of He will be