- 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 (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.
- 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 unit of resistance is ohm: 1W = 1VA-1.
- The resistance R of a conductor depends on its length l and constant cross-sectional area A through the relation.
where r, called resistivity is a property of the material and depends on temperature and pressure.
- Electrical resistivity of substances varies over a very wide range. Metals have low resistivity, in the range of 10-8Wm to 10-6Wm. 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 or current are electrons; in some cases e.g., 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.
j = nqv
where n is the number density (number per unit volume) of charge carriers each of charge q, and v is the drift velocity of the charge carriers. For electrons q = -e. If j is normal to a cross-sectional area A and is constant over the area, the magnitude of the current I through the area is (nev A).
- Using E = V/l, I = nev 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. If such collisions occur on an average at a time interval t,
vd = at = eEt/m
where a is the acceleration of the electron. This gives
- In the temperature range in which resistivity increases linearly with temperature, the temperature coefficient of resistivity a 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
(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 increases with I (even if temperature is kept fixed). A rectifier combines features
(a) and (b). A thyristor shows all the features (a), (b) and (c).
- When a source of emf e is connected to an external resistance R, the voltage Vext across R is given by
where r is the internal resistance of the source.
- (a) Total resistance R of n resistors connected in series is given by
R = R1 + R2 + …Rn
(b) Total resistance R of n resistors connected in parallel is given by
(a) First Rule (Junction Rule): At any junction of circuit elements, the sum of currents entering the junction must equal the sum of currents leaving it.
(b) Second Rule (Loop Rule): The algebraic sum of changes in potential around any closed loop must be zero.
- A voltmeter consists of a galvanometer (or resistance RG) in series with a high resistance R. It is put in parallel to the circuit element across which the voltage is to be measured. Because of its high (R + R @ R). It draws a very small current and thus does not disturb the circuit. If the full scale deflection of the galvanometer occurs for a current Io and the voltmeter is to have range Vo, we have
- An ammeter consists of a galvanometer (or resistance RG) and low resistance R in parallel. The effective resistance of the ammeter is
Because of its very low resistance, the ammeter placed in series in a circuit does not materially change the current in the circuit to be measured. If the full-scale deflection of the galvanometer occurs for current Io and the ammeter is to have a range Imax, we have
- The potentiometer is a device to compare potentials. Since the method involves a condition of no current flow, the device can be used to compare emfs of two sources.
- The Wheatstone bridge is an arrangement of four resistances - P, Q, R, S as shown in the text. The null-point condition is given by
using which the value of one resistance can be determined, knowing the other three resistances.
