Two material bars A and B of equal area of crosssection, are connected in series to a DC supply. A is made of usual resistance wire and B of an n-type semiconductor. (i) In which bar is drift speed of free electrons greater? (ii) If the same constant current continues to flow for a long time, how will the voltage drop across A and B be affected? Justify each error.

(a) Define the term ‘conductivity’ of a metallic wire. Write its SI unit. (b) Using the concept of free electrons in a conductor, derive the expression for the conductivity of a wire in terms of number density and relaxation time. Hence obtain the relation between current density and the applied electric field E.

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) 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.

(i) Deduce the relation between current I flowing through a conductor and drift velocity $v_{d}$ 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.

The temperature coefficient of resistivity, for two materials A and B, are 0.0031 / °C and 0.0068 / °C respectively. Two resistors R1 and R2, made from materials A and B, respectively, have resistances of 200 Ω and 100 Ω at 0°C. Show on a diagram, the 'colour code', of a carbon resistor, that would have a resistance equal to the series combination of R1 and R2, at a temperature of 100°C. (Neglect the ring corresponding to the tolerance of the carbon resistor).

A student connects a cell, of emf E2 and internal resistance r2 with a cell of emf E1 and internal resistance r1, such that their combination has a net internal resistance less than r1. This combination is then connected across a resistance R. Draw a diagram of the 'set-up' and obtain an expression for the current flowing through the resistance.

A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current I. It is found that when R = 4 Ω, the current is 1 A when R is increased to 9 Ω, the current reduces to 0.5 A. Find the values of the emf E and internal resistance r.

The potential difference across a resistor ‘r’ carrying current ‘I’ is Ir. (i) Now if the potential difference across ‘r’ is measured using a voltmeter of resistance ‘$R_{v}$’, show that the reading of voltmeter is less than the true value. (ii) Find the percentage error in measuring the potential difference by a voltmeter. (iii) At what value of $R_{v}$’, does the voltmeter measures the true potential difference?

In the two electric circuits shown in the figure, determine the readings of ideal ammeter (A) and the ideal voltmeter (V).

(i) Derive an expression for drift velocity of electrons in a conductor. Hence deduce Ohm’s law. (ii) A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts. Which of the following quantities remain constant in the wire ? (a) drift speed (b) current density (c) electric current (d) electric field Justify your answer.

A 100 V battery is connected to the electric network as shown. If the power consumed in the 2 Ω resistor is 200 W, determine the power dissipated in the 5 Ω resistor.

(i) Why do the 'free electrons', in a metal wire, 'flowing by themselves', not cause any current flow in the wire ? Define 'drift velocity' and obtain an expression for the current flowing in a wire, in terms of the 'drift velocity' of the free electrons. (ii) Use the above expression to show that the 'resistivity', of the material of a wire, is inversely proportional to the 'relaxation time' for the 'free electrons' in the metal.