Question

Hello the answer should be for the A-LEVEL student and the final answer in 2 signifcate figure

Answer 1

Given:

Length of wire = 1 km

Diameter of wire = 1 mm

Rsistivity of constantan = 4.9x10⁻⁷ Ωm

Resistivity of copper = 1.7 x 10⁻⁸ Ωm

Let's calculate the resistance of each material.

To find the resistance, apply the formula:

`R=(p\ast l)/(A)`

Where:

R is the resistance

p is the resistivity

l is the length of wire

A is the cross-sectional Area.

(a) Constantan:

Where:

p = 4.9x10⁻⁷ Ωm

l = 1 km = 1000 m

To find the cross sectional area, we have:

`A=(\pi d^2)/(4)=(\pi\ast(1\ast10^(-3)))/(4)=7.85\ast10^(-7)m^2`

Thus, we have:

`\begin{gathered} R=(p\ast l)/(A) \\ \\ R=(4.9\ast10^(-7)\ast1000)/(7.85\ast10^(-7)) \\ \\ R=623.88\Omega\approx620\Omega \end{gathered}`

Therefore, the resistance of constantan is 620 Ω.

(b) Resistance of copper:

Where:

p = 1.7 x 10⁻⁸ Ωm

l = 1 km = 1000 m

A = 7.85 x 10⁻⁷m²

Thus, we have:

`\begin{gathered} R=(p\ast l)/(A) \\ \\ R=(1.7\ast10^(-8)\ast1000)/(7.85\ast10^(-7)) \\ \\ R=21.6\text{ }\Omega\approx22\Omega \end{gathered}`

Therefore, the resistance of the copper is 22 Ω.

(c) We can see the resistance of the copper is less than the resistance of constantan.

Therefore, this means the constantan has a higher resistance than copper..

Therefore, the best material that is suited to make resistors will be the constantan .

ANSWERS:

(a) 620 Ω

(b) 22 Ω

(c) Constantan