Two metallic wires P₁ and P₂ of the same material and same length but different cross-sectional areas A₁ and A₂ are joined together and then connected to a source of emf. Find the ratio of the drift velocities of free electrons in the wires P₁ and P₂ if the wires are connected
(i) in series, and (ii) in parallel.
(i) in series, and (ii) in parallel.
Define relaxation time of the free electrons drifting in a conductor. How is it related to the drift velocity of free electrons ? Use this relation to deduce the expression for the electrical resistivity of the material.
Two cells of emfs E₁ & E₂ and internal resistances r₁ & r₂ respectively are connected in parallel. Obtain expressions for the equivalent.
(i) resistance and
(ii) emf of the combination
Two electric bulbs P and Q have their resistances in the ratio of 1 : 2. They are connected in series across a battery. Find the ratio of the power dissipation in these bulbs.
Two identical cells, each of emf E, having negligible internal resistance, are connected in parallel with each other across an external resistance R. What is the current through this resistance ?
A battery of emf 10 V and internal resistance 3 ohm is connected to a resistor. If the current in the circuit is 0.5 A, find :
(i) the resistance of the resistor;
(ii) the terminal voltage of the battery.
Two cells of emfs 1.5 V and 2.0 V having internal resistances 0.2Ω and 0.3Ω respectively are connected in parallel. Calculate the emf and internal resistance of the equivalent cell.
The plot of the variation of potential difference across a combination of three identical cells in series, versus current is shown below. What is the emf and internal resistance of each cell ?
An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of Nm. Calculate the potential energy of the dipole, if it has charge ± 8 nC.
In the circuit shown in the figure, find the current through each resistor.
Using the concept of drift velocity of charge carriers in a conductor, deduce the relationship between current density and resistivity of the conductor.
A network of resistors is connected to a 16 V battery with internal resistance of 1 Ω, as shown in the following figure. Compute the equivalent resistance of the network.
Two cells of emf and have internal resistance and . Deduce an expression for equivalent emf of their parallel combination.
A small metallic sphere carrying charge +Q is located at the centre of a spherical cavity in a large uncharged metallic spherical shell. Write the charges on the inner and outer surfaces of the shell. Write the expression for the electric field at the point P1.
Two point charges q and –2q are kept d distance apart. Find the location of the point relative to charge q at which potential due to this system of charges is zero.