Current through a given area of a conductor is the net charge passing per unit time through the area.
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 (from one terminal of the source to the other) is called the electromotive force, or emf, of the source.
The emf is not a force; it is the voltage difference between the two terminals of a source in open circuit.
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.
The resistance R of a conductor depends on its length l and cross-sectional area A.
Electrical resistivity of substances varies over a very wide range. Metals have low resistivity, in the range of 10-8 Ω m to 10-6 Ω m. Insulators like glass and rubber have 1022 to 1024 times greater resistivity. Semiconductors like Si and Ge lie roughly in the middle range of resistivity on a logarithmic scale.
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.
Current density j gives the amount of charge flowing per second per unit area normal to the flow.
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.
Ohm’s law is obeyed by many substances, but it is not a fundamental law of nature. It fails if
- V depends on I non-linearly
- the relation between V and I depends on the sign of V for the same absolute value of V
- The relation between V and I is non-unique
Kirchhoff’s Rules
- Junction Rule: At any junction of circuit elements, the sum of currents entering the junction must equal the sum of currents leaving it.
- Loop Rule: The algebraic sum of changes in potential around any closed loop must be zero.
The Wheatstone bridge is an arrangement of four resistances. 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.