EFFECTS OF TEMPERATURE
ON THE RESISTANCE OF
CARBON AND METAL FILAMENTS
OBJECT: -
To study the effect of temperature on the resistance of carbon and metal filaments.
APPARATUS: -
Sr. No. Name of Components Range No. Regd Remark
1. AMMETER
2. VOLMETER
3. RHEOSTAT
4. METAL FILAMENT LAMP
5. CARBON FILAMENT LAMP
THEORY: -
The resistance of various types of materials dependence on the temperature. The resistance of metal increases with the increase in its temperature because the temperature co-efficient of resistance for the metal is positive. The resistance of non-metals like carbon decreases as the temperature increases because the temperature co-efficient resistance is negative.
Hence, the temperature co-efficient of a material may be defined as the increase in resistance per ohm original resistance per rise in temperature.
R1 = Resistance at temperature = t1?C
R2 = Resistance at temperature = t2?C
R0 = Resistance at 0� c = 0?C
?0 = Temperature Co-efficient of at = 0?C
R2 = R0 [1 + ?0 t2] --- [1]
R1 = R0 [1 + ?0 t1] --- [2]
Dividing eq. [By eq. (ii)]
R2 R0 [1 + t2?0]
------- = ------------------- ---- [3]
R1 R0 [1 + t1?0]
In the above formula (iii) t, R1 are known, and the value of R2 is found out incidentally then t2 can be easily calculated as follows: -
? R2 [1 + ?0 t1]
------------------ = 1 + ?0 t2
R1
? R2 [1 + ?0 t1] � R1
------------------------- = ?0 t2
R1
? R2 [1 + ?0 t1] � R1
------------------------- = ?0 t2
R1
FOR METALS: -
If at t1 = 0 ?C, R1 = 75 ohms.
And ?0 = .0455 for metal
1 R2 R2
? t2 = --------- ------- - 1 + ----- t1
.0455 R1 R1
This can be further simplified as follows: -
R2 + ?0 R2 t1 - R1
? t2 = ------------------------
?0 R1
R2 - R1 + ?0 R2 t1
? t2 = ------------------------
?0 R1
R2 - R1 ?0 R2 t1
? t2 = ----------- + -------------
?0 R1 ?0 R1
R2 R2
? t2 = 1 / ?0 ----- - 1 + ---------- t1
R1 R1
FOR CARBON METALS: -
If at t1 = 20 ?C, R1 = 700 ohms.
And ?0 = - 0.0003
Then,
1 R2 R2
? t2 = ------------ ------ - 1 + ----- t1
- 0.0003 R1 R1
Now the value of temperature at various voltages is known, since R2 can be calculated from: -
V
R2 = ------------ Metal
Im
V
R2 = ------------ Carbon
Ic
PROCEDURE: -
1. Set up connections as per ckt dia.
2. Gradually increase voltage to the lamp with the help of rhestat.
3. Not down voltage applied to lamp.
4. Make calculations.
5. Draw graphs;-
(i) Resistances of carbon filaments. V/S temperature.
(ii) Resistance of metal filament. V/S temperature.
CONCLUSION: -