Question

A wire of uniform cross-section A and length L is cut into two equal parts. The resistance of each part becomes:
1. Double 2. Half 3. 4 times 4. ¼ times

Answer 1

Answer :-

(2) half ✓

To Find :-

Resistance of each part .

Explanation :-

According to the question

→ A wire has uniform cross-section area is A and length is L .

Hence its resistance is

$\implies \boxed{ \sf{ R = \frac{ \rho \: L}{A} \: }}$

now , according to the question

Its length cuts into two equal parts .

New length = L/2

hence its resistance is -

$\implies \: \sf{R' = \frac{ \rho \: \frac{L}{2} }{A} \: } \\ \\ \implies \sf{R' = \frac{ \rho \: L }{2A} \: } \\ \\ \implies \sf{\sf{R'} = \frac{1}{2} \: \: \frac{ \rho \: L }{A}} \: \: \: \: \\ \because \boxed{ \sf{ R = \frac{ \rho \: L }{A} \: }} \\ \therefore \: \\ \implies \boxed{\sf{ \sf{R'} = \frac{\sf{R}}{2} }}$

hence its resistance will becomes half .

and , resistivity of material will not change by changing the shape , also uniform cross-section area will not be change .

Answer 2

$\tt{\huge{\orange { ------------- }}} S.D$

QUESTION :

A wire of uniform cross-section A and length L is cut into two equal parts.

The resistance of each part becomes:

1. Double

2. Half

3. 4 times

4. ¼ times

SOLUTION :

We know that Resistivity is equal to $\rho \dfrac{L}{A}$

Where, L is the length of the wire and A is the cross Sectional Area.

Now in this question,

The wire is of uniform cross Sectional Area.

It is cut into two Equal parts.

Length of each part is L / 2

So resistance for each part becomes :

Resistivity = $\rho \dfrac{ \frac{L}{2}}{ A } = \rho \dfrac{L}{2A}$

Now dividing the first Resistivity with the second value of Resistivity, we get the following ratio :

=> 1 / 2

So the resistance of each part is 1 / 2.

So the answer is option 2.