(i) Derive an expression for drift velocity of free electrons.
(ii) How does drift velocity of electrons in a metallic conductor vary with increase in temperature ? Explain.
Define the term current density of a metallic conductor. Deduce the relation connecting current density (J) and the conductivity σ of the conductor, when an electric field E, is applied to it.
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.
A 9 V battery is connected in series with a resistor. The terminal voltage is found to be 8 V. Current through the circuit is measured as 5 A. What is the internal resistance of the battery?
Nichrome and copper wires of same length and same radius are connected in series. Current I is passed through them. Which wire gets heated up more ? Justify your answer.
The figure shows a plot of terminal voltage ‘V’ versus the current ‘i’ of a given cell. Calculate from the graph
(i) emf of the cell and (ii) internal resistance of the cell.
A cell of emf 4 V and internal resistance 1 W is connected to a d.c. source of 10 V through a resistor of 5 W. Calculate the terminal voltage across the cell during charging.
A circuit containing an 80 mH inductor and a 250 µF capacitor in series connected to a 240 V,100 rad/s supply. The resistance of the circuit is negligible.
(i) Obtain rms value of current.
(ii) What is the total average power consumed by the circuit ?
Derive an expression for electric field of a dipole at a point on the equatorial plane of the dipole. How does the field vary at large distances?
(i) Write two properties by which electric potential is related to the electric field.
(ii) Two point charges q₁ and q₂ separated by a distance of r₁₂ are kept in an external electric field. Derive an expression for the potential energy of the system of two charges in the field.
(i) Deduce the relation between current I flowing through a conductor and drift velocity of the electrons.
(ii) Figure shows a plot of current ‘I’ flowing through the cross-section of a wire versus the time ‘t’. Use the plot to find the charge flowing in 10 s through the wire.
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
(i) Derive an expression for drift velocity of free electrons.
(ii) How does drift velocity of electrons in a metallic conductor vary with increase in temperature ? Explain.
An inductor of 200 mH, capacitor of 400 µF and a resistor of 10 Ω are connected in series to ac source of 50 V of variable frequency. Calculate the
(a) angular frequency at which maximum power dissipation occurs in the circuit and the corresponding value of the effective current, and
(b) value of Q-factor in the circuit.