Title 3. CURRENT ELECTRICITY.pdf ✅

TOPIC-1 Electric Current & Cells Concepts Covered:  Electric current  Drift velocity  Ohm’s law  V-I characteristics, Resistivity and conductivity  Temperature dependence of resistance  Cells and their combinations. Revision Notes Electric current  Electric current is defined as the rate of flow of charge, across the cross section of a conductor, i.e., I dq dt = Flow of electric charges in metallic conductor  When an electric field is applied to a metal at certain points, free electrons experience force and start moving.  Drift velocity is an average velocity which is obtained by certain particles like electrons due to the presence of electric field.  Drift velocity =   v eE m v e d = − = = t t l where, relaxation time, here, charge of an el , ectron, = mass of an electron, = mean freepath, E = Electric m l field across conductor [Board 2019, 2023]   v eE m v e d = − = = t t l where, relaxation time, here, charge of an el , ectron, = mass of an electron, = mean freepath, E = Electric m l field across conductor   v eE m v e d = − = = t t l where, relaxation time, here, charge of an el , ectron, = mass of an electron, = mean freepath, E = Electric m l field across conductor  When electric current is set up in a conductor, electrons drift through the conductor with velocity vd, given as v I neA d = or I = neAvd [Board 2023] where, I = Electric current through the conductor, n = Number of free electrons per unit volume, A = Area of cross-section, e = Charge of electron  Mobility is the drift velocity of an electron when applied electric field is unity. Mobility, μ = v E d [Board 2023] or, m = e E m E e m τ τ / = Example-1 (a) Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 × 10–7 m2 carrying a current of 1.5A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is 9.0 × 103 kg/m3 , and its atomic mass is 63.5u. (b) Compare the drift speed obtained above with, (i) thermal speeds of copper atoms at ordinary temperatures, (ii) speed of propagation of electric field along the conductor which causes the drift motion. A Solution: (a) Molar mass of copper M = 63.5 g = 63.5 ×10–3 kg Density of copper ρ = 9 × 103 kgm–3 Number of copper atoms per unit volume n = ρ M × NA n = 9 10 6 0 10 3 23 3 × × × − . 63.5×10 = 8.5 × 1028 m–3 The drift speed vd is given by, vd = (I/neA) Now, e = 1.6 × 10–19C, A = 1.0 × 10–7 m2 , I = 1.5A. which gives, vd = 1.5 8.5×1028 19 7 ×× ×× 1 6 10 1 0 10 − − . . = 1.1 × 10–3 ms–1 = 1.1 mms–1 Learning Objectives After going through this chapter, the students will be able to learn:  Ohm's Law in conductors and hence define resistivity.  The power loss in current carrying conductors.  Potential difference and emf of a cell.  Combination of cells in series and in parallel.  Kirchhoff's law in electric circuits and derive the balanced condition of Wheatstone bridge. 3 CHAPTER CURRENT ELECTRICITY List of Topics Topic-1: Electric Current & Cells Topic-2 : Kirchhoff's Rules & Wheatstone Bridge