Question

what will be the new resitance of a wire if the radius of the wire has been increased by 5% of
its original value where its original resistance is 50 ohm​

Answer 1

Answer:

$\sf{The \ resistance \ will \ be \ of \ 47.5 \ \Omega}$

Given:

$\sf{Resistance \ is \ 50 \ \Omega}$

To find:

$\sf{The \ resistance \ after \ increasing \ the}$

$\sf{radius \ by \ 5\%}$

Solution:

$\boxed{\sf{Resistance \ \propto \ \dfrac{1}{Cross \ section \ area}}}$

$\sf{Hence, \ if \ the \ cross \ section \ area \ increases}$

$\sf{by \ 5\% \ then \ the \ resistance \ will \ decrease}$

$\sf{by \ 5\%}$

$\sf{\leadsto{5\% \ of \ 50=\dfrac{5}{100}\times50}}$

$\sf{\leadsto{5\% \ of \ 50 \ \Omega=2.5 \ \Omega}}$

$\sf{Hence,}$

$\sf{The \ new \ resistance=50-2.5}$

$\sf{\therefore{The \ new \ resistance=47.5 \ \Omega}}$

$\sf{The \ resistance \ will \ be \ of \ 47.5 \ \Omega}$

Answer 2

Answer:

⭐Given ⭐

✏Resistance is 50 Ω

⭐To find⭐

✏The resistance after increasing the radius by 5%

⭐Solution⭐

$\bold{\small{\fbox{\color{red} {Resistance ∝ 1/Cross section area }}}}$

Hence, the cross section increaseby 5% then the resistance will decrease by 5%

=>5% of 50= 100/5 ×50

=>5% of 50 Ω=2.5 Ω

➡Hence,

The new resistance=50−2.5

∴The new resistance=47.5 Ω

✍The resistance will be of 47.5 Ω✔

Step-by-step explanation:

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