A filament bulb (500 W, 100 V) is to be used in a 230 V main suply. When a resistance R is connected in series, it works perfectly and the bulb consumes 500 W. The value of R is : 

The potential difference (V_A – V_B) between the points A and B in the given figure is :

A parallel- plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constant k₁, k₂, k₃ and k₄ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

An electric dipole is placed at an angle of 30º with an electric field intensity 2 ×10⁵ N/C. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2cm, is

Three sound waves of equal amplitudes have frequencies (n –1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L meter long. The length of the open pipe will be