Resistance (R) of a copper wire of length l and cross-section A is given by the expression,
\(R = ρ\frac {l}{A}\)
Where,
ρ is resistivity of copper = 1.6 × 10–8 Ω m
R = 10 Ω,
radius of wire r = \(\frac {0.5}{2}\)mm = 0.25 mm = 0.00025 m
𝐴 = 𝜋𝑟2
A = 3.14×(0.00025)2
A = 0.000000019625 m2
⟹𝑙 = \(\frac {𝑅𝐴}{ρ}\)
⟹𝑙 = \(\frac {10×0.000000019625}{1.6×10^{−8}}\)
⟹𝑙 = 122.72 𝑚
If the diameter (radius) is doubled, the new radius r = 0.5 mm = 0.0005 m
𝐴 = 𝜋𝑟2
A = 3.14×(0.0005)2
A = 0.000000785 m2
So, the new resistance will be
\(𝑅^′=ρ\frac {𝑙}{𝐴}\)
\(R' = \frac {1.6×10^{−8} \times 122.72}{0.000000785 }\)
\(R'=2.5\ Ω\)
Now,
\( \frac {𝑅^′}{𝑅}=\frac {2.5}{10}\)
⟹ \( \frac {𝑅^′}{𝑅}=\frac {1}{4}\)
⟹ \(𝑅^′=\frac 14𝑅\)
Hence, the new resistance will become \(\frac 14\) times the original resistance.
Resistance is the measure of opposition applied by any object to the flow of electric current. A resistor is an electronic constituent that is used in the circuit with the purpose of offering that specific amount of resistance.
R=V/I
In this case,
v = Voltage across its ends
I = Current flowing through it
All materials resist current flow to some degree. They fall into one of two broad categories:
Resistance measurements are normally taken to indicate the condition of a component or a circuit.