Current Electricity
Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current
Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity
Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance
Internal resistance of a cell, potential difference and EMF of a cell, combination of cells in series and in parallel
Kirchhoff’s laws and simple applications
Wheatstone bridge, metre bridge
Potentiometer −
SUMMARY
1. Current through a given area of a conductor is the net charge passing per unit time through the area.
2. To maintain a steady current, we must have a closed circuit in which an external agency moves electric charge from lower to higher potential energy. The work done per unit charge by the source in taking the charge from lower to higher potential energy (i.e., from one terminal of the source to the other) is called the electromotive force, or emf, of the source. Note that the emf is not a force; it is the voltage difference between the two terminals of a source in open circuit.
3. Ohm’s law: The electric current I flowing through a substance is proportional to the voltage V across its ends, i.e., V ∝ I or V = RI, where R is called the resistance of the substance.
4. The resistance R of a conductor depends on its length l and constant cross-sectional area A through the relation.
5. In most substances, the carriers of current are electrons; in some cases, for example, ionic crystals and electrolytic liquids, positive and negative ions carry the electric current.
6. Current density j gives the amount of charge flowing per second per unit area normal to the flow, j = nq vd where n is the number density (number per unit volume) of charge carriers each of charge q, and vd is the drift velocity of the charge carriers.
7. Using E = V/l, I = nevd A, and Ohm’s law, one obtains the proportionality between the force eE on the electrons in a metal due to the external field E and the drift velocity vd (not acceleration) can be understood, if we assume that the electrons suffer collisions with ions in the metal, which deflect them randomly.
8. In the temperature range in which resistivity increases linearly with temperature, the temperature coefficient of resistivity α is defined as the fractional increase in resistivity per unit increase in temperature.
9. Ohm’s law is obeyed by many substances, but it is not a fundamental law of nature. It fails if (a) V depends on I non-linearly. (b) the relation between V and I depends on the sign of V for the same absolute value of V. (c) The relation between V and I is non-unique. An example of (a) is when ρ increases with I (even if temperature is kept fixed). A rectifier combines features (a) and (b). GaAs shows the feature (c).
10. Kirchhoff’s Rules – (a) Junction Rule: At any junction of circuit elements, the sum of currents entering the junction must equal the sum of currents leaving it. (b) Loop Rule: The algebraic sum of changes in potential around any closed loop must be zero.
11. The potentiometer is a device to compare potential differences. Since the method involves a condition of no current flow, the device can be used to measure potential difference; internal resistance of a cell and compare emf’s of two sources.
