If the cross-sectional area of X is 5.0×10*-6 m² , and the length of X is 1.2m.The potential difference of X is 8V.Current of X is 2A.Calculate its resistivity.
Answers
Answer:
resistance = resistivity (rho)* length/ area
since resistance= potential/current
so we get rho = potential* area/ current* length
since rho = 8*5*10^(-6)/ 2*1.2
since , resistivity= 1.66* 10^(-5)
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Given that,
Area of cross-section (A) = 5.0 × 10^(-6) m², length (l) = 1.2 m, Potential difference (V) = 8 V and current (I) = 2A
From Ohms law
The potential difference (V) across the ends of the wire is directly proportional to current (I) flowing through that wire, provides the temperature remains the same.
V = IR
Here, V = Potential difference, I = current and R = resistance
R = V/I
R = 8/2 = 4
Now,
The resistance of the conductor (wire) is directly proportional to the length of wire i.e. R ∝ l
Inversely proportional to area of cross-section of wire i.e. R ∝ 1/A
R ∝ l/A
If we remove the sign of proportionality we use a constant i.e. p (rho)
R = p (l)/A
Here, R = resistance, p = rho (resistivity), l = length and A = Area of cross-section
Substitute the known values
4 = p (1.2)/[5.0 × 10^(-6)]
4 = p (0.24 × 10^6)
4/(0.24 × 10^6) = p
16.67 × 10^(-6) = p
1.67 × 10^(-5) = p
Therefore, the resistivity of X is 1.67 × 10^(-5) Ω m