A wire of resistance R is cut into 5 equal parts and connected in parallel. If the equivalent resistance of this combination is R', calculate the ratio R/R'. Created by ananyaa30121995V. Physics

AnsWer :25 : 1.To FinD :Calculate the ratio R/R'SolutioN :Let,Resistance be R.Size of Wire A to B.☛Condition :When We cutting a wire 5 Equal part its resistance become R/5 and When We connect in parallel combination it become 5/R.We have Formula for parallel combination → 1/R = 1/R1 + 1/R2 + 1/R3 + ..+ 1 /Rn.★ Diagram.★ Let's Find the ratio of R/R'.Therefore, the ratio of R/ R' is 25 : 1.

R'...

amitkumar44481

Verified answer

AnsWer :

25 : 1.

To FinD :

Calculate the ratio R/R'

SolutioN :

Let,

Resistance be R.
Size of Wire A to B.

☛Condition :

When We cutting a wire 5 Equal part its resistance become R/5 and When We connect in parallel combination it become 5/R.
We have Formula for parallel combination → 1/R = 1/R1 + 1/R2 + 1/R3 + ..+ 1 /Rn.

★ Diagram.

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\put(0,0){\line(1,0){30}}\put(-3,0){$A$}\put(31,0){$B$}\put(1,-5){$\frac{R}{5}$}\put(6,-5){$\frac{R}{5}$} \put(12,-5){$\frac{R}{5}$}\put(18,-5){$\frac{R}{5}$}\put(24,-5){$\frac{R}{5}$}\end{picture}$

★ Let's Find the ratio of R/R'.

$\tt \longmapsto\dfrac{1}{R'_Parallel }= \dfrac{5}{R} + \dfrac{5}{R} + \dfrac{5}{R} + \dfrac{5}{R} +\dfrac{5}{R}$

$\tt \longmapsto \dfrac{1}{R'} = \dfrac{25}{R}$

$\tt \longmapsto R' = \dfrac{R}{25}$

$\tt \longmapsto \dfrac{R}{R'} = 25.$

Therefore, the ratio of R/ R' is 25 : 1.

CunningKing

Verified answer

GiVeN :-

A wire of resistance R is cut into 5 equal parts and connected in parallel.
Equivalent resistance of this combination is R'.

To DeTeRmInE :-

The ratio R/R'.

AcKnOwLeDgEmEnT :-

$\bullet$ As the wire is cut into 5 equal parts, so the resistance of each part becomes R/5.

$\bullet$ For connections in parallel,

$\sf{\dfrac{1}{R_{Equivalent}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+...+\dfrac{1}{R_4} }$

SoLuTiOn :-

Putting the values :-

$\sf{\dfrac{1}{R_{Equivalent}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+...+\dfrac{1}{R_4} }$

$\displaystyle{\sf{\longmapsto \frac{1}{R'} =\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5}+\frac{1}{R/5} }}\\\\\displaystyle{\sf{\longmapsto \frac{1}{R'}=\frac{5}{R}+\frac{5}{R} +\frac{5}{R} +\frac{5}{R} +\frac{5}{R} }}\\\\\displaystyle{\sf{\longmapsto \frac{1}{R'}=\frac{25}{R} }}\\\\\displaystyle{\sf{\longmapsto R'=\frac{R}{25} }}$

$\rule{120}2$

Now,

$\displaystyle{\sf{\frac{R}{R'}=\frac{R}{\frac{R}{25} } }}\\\\\\\displaystyle{\sf{\longmapsto \frac{R}{R'}=R \times \frac{25}{R} }}\\\\\\\boxed{\displaystyle{\sf{\longmapsto \frac{R}{R'}=\frac{25}{1} }}}$

Hence, the ratio of R/R' is 25 : 1.

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Answers & Comments

Verified answer

AnsWer :

To FinD :

SolutioN :

Therefore, the ratio of R/ R' is 25 : 1.

Verified answer

GiVeN :-

To DeTeRmInE :-

AcKnOwLeDgEmEnT :-

SoLuTiOn :-

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