Write the expression for the drift velocity of charge carriers in a conductor of length l across which a potential difference V is applied.
(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.
Using the concept of drift velocity of charge carriers in a conductor, deduce the relationship between current density and resistivity of the conductor.
How does the random motion of free electrons in a conductor get affected when a potential difference is applied across its ends ?
Draw a plot showing the variation of resistivity of a (i) conductor and (ii) semiconductor, with the increase in temperature. How does one explain this behaviour in terms of number density of charge carriers and the relaxation time ?
The current, in the LCR circuit shown in the figure is observed to lead the voltage in phase. Without making any other change in the circuit, a capacitor,of capacitance C₀, is (appropriately) joined to the capacitor C. This results in making the current,in the ‘modified’ circuit, flow in phase with theapplied voltage.
Draw a diagram of the ‘modified’ circuit and obtain an expression for C₀ in terms of ω, L and C.
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.
Obtain the expression for the potential due to an electric dipole of dipole moment p at a point ‘d’ on the axial line.
Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figure.
An inductor L of inductance is connected in series with a bulb B and an ac source. How would brightness of the bulb change when
(i) number of turns in the inductor is reduced,
(ii) an iron rod is inserted in the inductor and
(iii) a capacitor of reactance is inserted in series in the circuit. Justify your answer in each case.
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.
(i) When an ac source is connected to an ideal inductor shows that the average power supplied by the source over a complete cycle is zero.
(ii) A lamp is connected in series with an inductor and an ac source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor ? Explain.