3.16 Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables. ( <math><msub><mrow><mrow><mi mathvariant="bold-italic">ρ</mi></mrow></mrow><mrow><mrow><mi mathvariant="bold-italic">A</mi><mi mathvariant="bold-italic">l</mi></mrow></mrow></msub></math> = 2.63 × 10–8 Ωm, <math><msub><mrow><mrow><mi mathvariant="bold-italic">ρ</mi></mrow></mrow><mrow><mrow><mi mathvariant="bold-italic">C</mi><mi mathvariant="bold-italic">u</mi></mrow></mrow></msub></math> = 1.72 × 10–8 Ω m, Relative density of Al = 2.7, of Cu = 8.9.)

3.16 Given, resistivity of aluminium, ρ1 = 2.63 ×10-8 ΩmResistivity of copper, ρ2 = 1.72 ×10-8 ΩmRelative density of aluminium = 2.7Relative density of copper = 8.9For Aluminium wire: Letl1 = length, m1 = mass, R1 = resistance, A1 = cross-section area, ρ1 = densityFor Copper wire: Letl2 = length, m2 = mass, R2 = resistance, A2 = cross-section area, ρ2 = densityFrom the relation R = ρlA , we getR1=ρ1l1A1 ………(1), andR2=ρ2l2A2 ………(2)It is given R1 = R2 and l1 = l2 . HenceA1A2 = ρ1ρ2 = 2.631.72 ( 10-8 cancel each other)From the relation mass = volume ×relativedensity = length × cross sectional area × relative density, we getm1=l1A1d1 and m2=l2A2d2 , where d1 = relative density of aluminium and d2 = relative density of copperm1m2=l1A1d1l2A2d2 = A1d1A2d2 = 2.631.72×2.78.9 = 0.464It can be inferred from this ratio that m1 is less than m2 . Hence, aluminium is preferred as overhead power cables over copper.

Ask & Answer Question

Physics Ncert Solutions Class 12th Physics Class 12th Electricity

3.16 Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables. ( $ρ_{A l}$ = 2.63 × 10^–8 Ωm, $ρ_{C u}$ = 1.72 × 10^–8 Ω m, Relative density of Al = 2.7, of Cu = 8.9.)

4 Views | Posted 6 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

6 months ago

3.16 Given, resistivity of aluminium, $ρ_{1}$ = 2.63 $\times 10^{- 8}$ Ωm

Resistivity of copper, $ρ_{2}$ = 1.72 $\times 10^{- 8}$ Ωm

Relative density of aluminium = 2.7

Relative density of copper = 8.9

For Aluminium wire: Let

$l_{1}$ = length, $m_{1}$ = mass, $R_{1}$ = resistance, $A_{1}$ = cross-section area, $ρ_{1}$ = density

For Copper wire: Let

$l_{2}$ = length, $m_{2}$ = mass, $R_{2}$ = resistance, $A_{2}$ = cross-section area, $ρ_{2}$ = density

From the relation R = $\frac{ρ l}{A}$ , we get

$R_{1} = \frac{ρ_{1} l_{1}}{A_{1}}$ ………(1), and

$R_{2} = \frac{ρ_{2} l_{2}}{A_{2}}$ ………(2)

It is given $R_{1}$ = $R_{2}$ and $l_{1}$ = $l_{2}$ &n

...more

3.16 Given, resistivity of aluminium, $ρ_{1}$ = 2.63 $\times 10^{- 8}$ Ωm

Resistivity of copper, $ρ_{2}$ = 1.72 $\times 10^{- 8}$ Ωm

Relative density of aluminium = 2.7

Relative density of copper = 8.9

For Aluminium wire: Let

$l_{1}$ = length, $m_{1}$ = mass, $R_{1}$ = resistance, $A_{1}$ = cross-section area, $ρ_{1}$ = density

For Copper wire: Let

$l_{2}$ = length, $m_{2}$ = mass, $R_{2}$ = resistance, $A_{2}$ = cross-section area, $ρ_{2}$ = density

From the relation R = $\frac{ρ l}{A}$ , we get

$R_{1} = \frac{ρ_{1} l_{1}}{A_{1}}$ ………(1), and

$R_{2} = \frac{ρ_{2} l_{2}}{A_{2}}$ ………(2)

It is given $R_{1}$ = $R_{2}$ and $l_{1}$ = $l_{2}$ . Hence

$\frac{A_{1}}{A_{2}}$ = $\frac{ρ_{1}}{ρ_{2}}$ = $\frac{2.63}{1.72}$ ( $10^{- 8}$ cancel each other)

From the relation mass = volume $\times r e l a t i v e d e n s i t y$ = length $\times$ cross sectional area $\times$ relative density, we get

$m_{1} = l_{1} A_{1} d_{1}$ and $m_{2} = l_{2} A_{2} d_{2}$ , where $d_{1}$ = relative density of aluminium and $d_{2}$ = relative density of copper

$\frac{m_{1}}{m_{2}} = \frac{l_{1} A_{1} d_{1}}{l_{2} A_{2} d_{2}}$ = $\frac{A_{1} d_{1}}{A_{2} d_{2}}$ = $\frac{2.63}{1.72} \times \frac{2.7}{8.9}$ = 0.464

It can be inferred from this ratio that $m_{1}$ is less than $m_{2}$ . Hence, aluminium is preferred as overhead power cables over copper.

less

0 Upvotes 0 Downvotes

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question