calculate the resistance of a metal wire of length 2m and area of cross section 1.55 x 10^-6 m^2, if the resistivity of the metal be 2.8 x 10^-8 ohm m.
Answers
Explanation:
Length of metal wire = 2m
Area of cross section = 1.55 \times 10^{-6} m^{2}1.55×10
−6
m
2
Resistivity of metal = 2.8 \times 10^{-8} \text { ohm } \mathrm{m}2.8×10
−8
ohm m
We have to find the resistance of metal wire.
L=2m
A= 1.55 \times 10^{-6} m^{2}1.55×10
−6
m
2
\bold{\rho=\frac{R A}{L}}ρ=
L
RA
Therefore,
\bold{\mathrm{R}=\frac{\rho L}{A}}R=
A
ρL
Now, let us substitute all the known values in the above expression.
We get,
R=\frac{2.8 \times 10^{-8} \times 2}{1.55 \times 10^{-6}}R=
1.55×10
−6
2.8×10
−8
×2
By simplification we get the above expression as,
\begin{gathered}\begin{array}{l}{R=\frac{560}{1.55 \times 10^{-2}}} \\ {R=3.61 \times 10^{-2}}\end{array}\end{gathered}
R=
1.55×10
−2
560
R=3.61×10
−2
Hence resistance of the metal wire= 3.61 \times 10^{-2}3.61×10
−2