Question

a wire of resistance R is cut into 10 equal parts which are joined in parallel find new resistance


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Answer 1

$\frac{1}{100}r\: \: is \: the \: new \: resistance.$

Please refer the above photograph for the used process.

SOLUTION :-

• Resistance of the given wire is R.
• 
  

• The wire is cut into 10 pieces.
• 
  

So,

• The resistance of each of the ten new resistors will be equal to
• 
  

$\frac{r}{10}\: \: \:ohms$

.....(i)

Now,

• These 10 parts are connected in parallel.
• 
  

Accordingly :-

• From Ohm's law we can derive a relation for the resistors connected in parallel.

• The relation is as follows :-

$\frac{1}{r(eq)} =\frac{1}{r1}+\frac{1}{r2} ..... +\frac{1}{rn}$

In this case :-

• There are 10 resistors with equal resistances of R/10 ohm.
• 
  

So,

$\frac{1}{r(eq)} =\frac{1}{r}+\frac{1}{r} ......10times. \\ \\ (as\: r1 = r2 = r3...... = r10) \\ \\ now \\ \\\frac{1}{r(eq)} =\frac{10}{r}\\ \\ r(eq) =\frac{r}{10}$

Now,

• In this case 'r'  is equal to R/10

{From part...... (i)}

So,

Putting the value we get :-

$r(eq) =\frac{\frac{r(c)}{10}}{10}\\ \\ r(eq) = \:\frac{r(c)}{100}$

Where,

• r(c)  refers to capital r that is R.

So,

• The relative or equivalent or new resistance of the system is 1/100 of the resistance of the initial wire.

So,

☸️R(eq)  = R/100

• Thanks!

Answer 2

HERE IS UR ANSWER......