Effect of temperature upon resistance: Usually, a metallic conductor has a crystalline structure in which its various atoms in form of positive ions are fixed at their respective places as shown in fig. 16. 7.

Free electrons move in the space between these atoms. During the course of their motion, they continuously collide with the atoms. After collision they scatter in various directions. When we apply a potential across the ends of the conductor, the free electrons, in addition to their random motion, have a directed motion with a velocity known as drift velocity. The current flows through the conductor due to this velocity. The opposition to the flow of current is caused by the collision of free electrons with the atoms of the conductor because after each collision the direction of motion of the electron randomly changes which slows down the drift velocity.

More frequently electrons collide with the atoms; the larger is opposition or resistance in the flow of current. When the temperature of the conductor rises, average speed to the random motion of the free electrons increases which enhances the rate of collision of electrons and the atoms. This causes an increase in the resistance of the conductor. The increase in resistance is directly proportional to the increase of temperature. If R₀ is the resistance at 0 ⁰C and  at t ⁰C, then we can write as

resistance-per ohm_per kelvin

Here a is a constant which is the rate of increase in resistance per ohm per Kelvin.

Eq. 16.4 suggest that by taking measurements of the resistance of a conductor of known value of a at different temperatures, it is possible to measure the temperature. This is the principle on which a resistance thermometer works.

Resistance thermometer

The conductor used in resistance thermometer is usually a platinum wire the end of which are welded with thick copper wire (Fig. 16.8). before measuring the temperature of a substance, the thermometer is placed in melting ice and its resistance at 0 ⁰C is measured. Let it be R₀ ohm. Then the bulb of the thermometer is placed into the substance whose temperature is to be measured. The resistance of the platinum wire is again measured. Let this time its value is  ohm. According to Eq. 16.4.


a platinum-resistance-thermometer

Fig. 16.8: a platinum resistance thermometer

Series And Parallel Combination Of Resistances

There are two basic methods b which resistances are connected in a circuit. One method is known as series combination and the other as parallel combination.

  1. Series combination of resistances 
  1. In this method resistances are connected end to end and the circuit thus formed provides only one path for the flow of current (Fig. 16.9).
  2. In this arrangement, the magnitude of current that flows through each individual resistor is the same.
  3. In series combination, the sum of voltages across each of the resistors is equal to the voltage of the battery connected across the combination. In Fig. 16. 9, if the voltage of the battery is

current passing through the resistors

path for the flow of current

Fig. 16.9

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