Measurement of Resistance

Ohm’s law and resistance
(a) Statement of Ohm’s Law. Ohm’s Law states that the electric current I flowing through a given conductor is directly proportional to the potential difference (voltage) V across its ends (provided that the physical conditionsâ€”temperature, pressure, of the conductor remain same).

where R is a constant of proportionality. It is called the resistance of the conductor. The unit of resistance, volt per ampere, is given a special name ohm and a Greek symbol Î© (Omega).

Resistance and specific resistance (resistivity)
The property of a conductor to oppose the flow of charges through it, is called its resistance.

The resistivity depends upon :
(i) Nature of material
(ii) Temperature of material
(iii) Pressure or mechanical stress.
The resistivity does not depend upon the dimensions of conductor, on which resistance depend, and mechanical deformation like stretching, etc.

Conductance and specific conductance (conductivity)
Reciprocal (inverse) of resistance, is called conductance. It is represented by the symbol G. Its S.I. unit is mho or siemens (S).

Reciprocal of resistivity, is called conductivity. It is represented by the symbol Ïƒ Its S.I. unit is ohm-1   m-1   or mho m-1  or Sm-1.

Effect of temperature on resistance
Resistance of all conductors is found to increase with increase in temperature of the conductor.

or
where a is constant of proportionality. It is called temperature coefficient of resistance of the material of the conductor.

Series combination of resistance (resistors)
(a) Description. When second end of first resistor be connected to first end of second resistor, and so on, the resistors are said to form a series combination. The first end of first resistor and the second end of last resistor is connected to the two terminals of a battery (source of e.m.f.) same current flows through all the resistors in series combination.
(b) Calculation. shows three resistors of resistances r1,  r2 and r3  ohm connected in series.

The combination is connected to the terminals of a battery of potential difference V. Same current I flows through all the resistors, which have potential difference V1,V2  and V3  across them. V is the potential difference across the combination.

(d) Explanation. In series combination, the effective length of resistor increases. As Râˆ?l, resistance increases in series combination.
(e) Series combination gives more resistance. Hence to get maximum resistance from given resistors, they have to connected in series.

Parallel combinations of resistance (resistors)
(Ð°) Description. When first end of all resistors are connected to one common point and second end to other common point, the resistors are said to form a parallel combination. The two common ends are connected to the two terminals of a battery (source of e.m.f.) same potential difference develops across all resistors.
(b) Calculation.  shows three resistors of resistance r1,  r2 and r3ohm connected in parallel.
The combination is connected to the terminals of a battery of potential difference V. All resistors have same potential difference V.  I1,I2  and I3 respectively is the current through the resistors. I is the total current in the combination.

(d) Explanation. In parallel combination, the effective area of cross section increases. As R âˆ? 1/A  resistance decreases in parallel combination.
(e) The parallel combination gives less resistance. Hence, to get minimum resistance from the given resistors, they have to connect in parallel.

Wheatstone bridge
(a) Description. A Wheatstone bridge consists of four resistors of resistances P, Q, R and S connected
so as to form a quadrilateral (bridge) ABCD.

One pair of opposite junctions (B and D) is connected through a galvanometer (G) and the other pair of opposite junctions (A and C) is connected through a cell (E) and key (K).
The values of resistances P, Q, R and S are so adjusted that the galvanometer shows no deflection on closing key K. It means that no current is flowing in arm BD and hence potential at B is equal to the potential at D. In this condition, the bridge is P R
said to be balanced. For balanced Wheatstone bridge P/Q = R/S
(b) Calculation. Let in balanced bridge, same current I1  flow through P and Q and same current I2 flow through R and S

(c) Applied Forms. The Wheatstone’s bridge has two applied forms :
1. Metre Bridge or Slide Wire Bridge.
2. Post Office Box.

A Short Description of Metre Bridge
(a) Description
Slide wire bridge or metre bridge is the practical form of Wheatstone bridge. Usually, P and Q are called ratio gums of fixed resistance, R is an adjustable or variable resistance of known value. Q is replaced by an unknown resistance X in  and balance point is obtained at D on the metre bridge wire. Since the bridge uses 1 metre long wire, it is called metre bridge. Since a jockey is slided over the wire, it is called a slide wire bridge.