Question

Calculate the length of wire.
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Answer 1

L = 169.5 m

Step-by-step explanation:

Using Ohm's Law:

V = IR

where,

V = Voltage = 1.5 V

I = Current = 10 mA = 0.01 A

R = Resistance = ?

Therefore,

1.5 V = (0.01 A)R

R = 150 Ω

But the resistance of a wire is given by the following formula:

`R = (\rho L)/(A)`

where,

ρ = resistivity = 1 x 10⁻⁶ Ω.m

L = length of wire = ?

A = cross-sectional area of wire = πr² = π(0.6 mm)² = π(0.6 x 10⁻³ m)²

A = 1.13 x 10⁻⁶ m²

Therefore,

`150\ \Omega = ((1\ x\ 10^(-6)\ \Omega .m)L)/(1.13\ x\ 10^(-6)\ m^2)\\\\L = (150\ \Omega(1.13\ x\ 10^(-6)\ m^2))/(1\ x\ 10^(-6)\ \Omega .m)\\\\`

L = 169.5 m