Calculate the length of a constantan wire of cross- sectional area 4 π x 10-8m2 and resistivity 1.1 x 10-6 Ω m required to construct a standard resistor of ...
Question 1 Report
Calculate the length of a constantan wire of cross- sectional area 4 π x 10-8m2 and resistivity 1.1 x 10-6 Ω m required to construct a standard resistor of resistance 21 Ω. [Take π = 22/7]
Answer Details
The resistance of a wire is given by the formula:
R = (ρ * L)/A
Where R is resistance, ρ is resistivity, L is the length of the wire and A is the cross-sectional area of the wire.
To find the length of the constantan wire required to construct a standard resistor of resistance 21Ω, we rearrange the formula to get:
L = (RA)/ρ
Substituting the given values, we have:
L = (21 * 4π x 10^-8)/ (1.1 x 10^-6)
L = 0.76 meters
Since the value of π was given as 22/7, we use the approximate value of π = 3.14 in the calculation.
Therefore, the length of the constantan wire required to construct a standard resistor of resistance 21 Ω is 0.76 meters.
So, the correct option is (b) 2.40 m.
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