Question

A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10^-8 ohm m.
What will be the length of this wire to make its resistance to 10 ohm.
How much does the resistance change if the diameter is doubled?​

Answer 1

${\bold{\boxed{\sf{\red{ANSWER}}}}}$

The length of wire = 122 m

${\bold{\boxed{\sf{\red{GIVEN}}}}}$

• A copper wire has diameter = 0.5 mm

resistivity of the wire = 1.6 x 10^-8 ohm m.

• Resistance (R) = 10 ohm

${\bold{\boxed{\sf{\red{FORMULA}}}}}$

• The resistance of a conductor =

$R = \rho \times \frac{l}{A}$

Where,

R = Resistance of wire

ρ = Resistivity of wire

l = length of wire

A = Area of cross section of wire

${\bold{\boxed{\sf{\red{SOLUTION}}}}}$

• Radius of the circle =

$\frac{0.5}{2} = 0.25mm = 0.25 \times {10}^{ - 3} m$

Area of the Circle =

$\pi \: {r}^{2} = \frac{22}{7} \times {(0.25 \times {10}^{ - 3} )}^{2} \\ \implies \: \frac{22 \times 0.0625 \times {10}^{ - 6} }{7} \: {m}^{2}$

NOW

$R = \rho \times \frac{l}{A} \\ \implies \: l \: = \frac{R \times A}{\rho} \\ \implies \: l = \frac{10 \times 22 \times 0.0625 \times {10}^{ - 6} }{7 \times 1.6 \times {10}^{ - 8} } \\ \implies \: l = 122 \: m$

The length of wire = 122 m