Series combination of resistors
The current across each circuit element is same, but potential difference is different & proportional to resistance of that part.
i.e. I = I1 = I2 = I3 & V1 = IR1, V2 = IR2, V3 = IR3 & R series = R1 + R2 + R3
Zero α for Nichrome, constantan & Manganin
i.e. there is appreciably no change (or very slight change) in R with temperature.
1. Constantan (or Eureka) ≡ Cu 60% & Ni 40%
2. Manganin ≡ Cu 84%, Mn 12% & Ni 4%
3. Nichrome ≡ Ni 67.5%, Cr 15%, Fe 16% & Mn 1.5%
– ve α for electrolytes
Cause of decrease in R with increase in temp. for electrolytes is decrease in viscosity.
– ve α for semiconductors
On heating semiconductors the number density of free electrons increases & τ decreases. But the effect of increase in ‘n’ is stronger than decrease in relaxation time (τ). Hence net effect is increase in ‘n’ which decreases resistance.
^Error in exponential form
Differentiating both sides we can write
The maximum value of fractional error will be
+ ve α for metals & alloys
With the increase in temperature of metals & alloys thermal agitation increases & hence the rate of collision increases. As a result the average time t between the successive collision decreases & hence the drift speed decreases, consequently the resistivity of metals increases.
Temperature variation of resistance
On heating a material its resistivity changes, which changes the electrical resistance of the material. The electrical resistivity at temperature T can be calculated by using relation: ρT = ρ0 (1+ αT)
Resistance of a wire on stretching
(a) increases n2 times original resistance if length is increased n times.
(b) decreases n4 times if the radius of a wire is increased n times.
Provided mass, density & resitivity wire are kept fixed.
Resistance of various geometries
Relations 1 to 4 are across length & relations 5 is for radial flow.
Above results are valid for uniform resistivity ρ only.
Electric resistance
Depends upon the nature of material, shape & size, physical state like temperature, pressure, type & extent of impurity etc. of conductor. However r depends upon all above factors except on shape & size.
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