Obtain the expression for the energy density of magnitude field B produced in the inductor.

Show that in the free oscillations of an LC circuit, the sum of energies stored in the capacitor and the inductor is constant in time.

(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 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.

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.

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

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?

(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.

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.

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) 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.

(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) When an ac source is connected to an ideal capacitor show that the average power supplied by the source over a complete cycle is zero. (ii) A lamp is connected in series with a capacitor.Predict your observation when the system is connected first across a dc and then an ac source.What happens in each case if the capacitance of the capacitor is reduced ?

A voltage V = V₀ sin ωt is applied to a series LCR circuit. Derive the expression for the average power dissipate over a cycle.Under what conditions is (i) no power dissipated even though the current flows through the circuit, (ii)maximum power dissipated in the circuit ?

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.