Question

A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of thid combination is R' then the ratio R/R' is

Answer 1

Answer:

the ratio of R / R' will be 25

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Answer 2

Given :-

• A piece of wire of resistance R is cut into five equals part.so, resistance of each part of wire will be $\rm\:\dfrac{R}{5}$.

• Five piece of wire,each piece of wire having resistance of $\rm\:\dfrac{R}{5}$ are connected in parallel to give the equivalent resistance R' .

To find :-

• The ratio $\rm\:\dfrac{R}{R'}$

Solution :-

we know that,

$\small\blue{\bigstar}\:\:{\underline{\boxed{\bf\pink{\dfrac{1}{R'}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+\dfrac{1}{R_4}+\dfrac{1}{R_5}}}}}$

$\rm\longrightarrow\:\dfrac{1}{R'}=\dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}$

$\rm\longrightarrow\:\dfrac{1}{R'}=\dfrac{5+5+5+5+5}{R}$

$\rm\longrightarrow\:\dfrac{1}{R'}=\dfrac{25}{R}$

Now,

⸕ Multiplying both sides by R.

$\rm\longrightarrow\:\dfrac{1}{R'}\times{R}=\dfrac{25}{\cancel{R}}\times{\cancel{R}}$

$\rm\longrightarrow\:\dfrac{R}{R'}=25$

Hence,the ration of R/R' will be 25.

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\red{More\:Information}}}}$

Resistance in parallel :- When two or more resistances are connected between the same two points then,they are said to be connected in parallel.

For example :- If a number of resistance R1,R2, R3..... etc are connected in parallel then their combined resistance R will be

1/R = 1/R1 + 1/R2 + 1/R3 +.....