Question

The resistance of a wire is 4 ohm. Calculate its new resistance if the radius of the wire is one-third of the original wire




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Answer 1

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

The resistance of a wire is 4 ohm. Calculate its new resistance if the radius of the wire is one-third of the original wire ?

$\mathtt{\huge{\underline{\green{Answer:-}}}}$

✏ The new resistance of wire is 12 Ω .

$\mathtt{\huge{\underline{\pink{Solution:-}}}}$

Given :-

• The resistance of a wire is 4 ohm.

• The radius of the wire is one-third of the original wire.

To Find :-

• The new resistance of wire.

Theory Involved :-

Resistance of a conductor is the property by virtue of which it opposes the charge through it.

R = $\dfrac{V}{I}$

S.I. unit of resistance :- 1 Ω = 1 VA-¹

The resistance of conductor is directly proportional to its length;

R ∝ l .......... (1)

The resistance of conductor is inversely proportional to its area of cross section ;

R ∝ $\dfrac{l}{a}$........... (2)

From 1 & 2 ,

R = p $\</em></strong><strong><em>d</em></strong><strong><em>frac</em></strong><strong><em>{l}{a}$

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Calculation :-

According to the question,

The resistance of wire = 4 Ω

Let the area be r;

So, The Area of cross-section = r

Using resistivity Formula;

R = p $\frac{l}{a}$

➡ 4 = p $\frac{l}{r}$

➡ 4 r = p I

➡ I = 4r/p

Now,

The radius of the wire is one-third of the original wire. So, new resistance

When R = 1/3 r,

=> R = p. l/a

=> R = p . 4r/a

=> R = p . 4r/pa

=> R = 4r/a

We know,

Area a = r/3

=> R = 4r/r/3

=> R = 4× 3

=> R = 12

➡ R = 12 Ω

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Answer 2

Answer:

Explanation:

Resistance= (pl)/a

l=length of wire

a=area of wire

Wire is doubled so length will be doubled.

Let's assume R initial resistance..

R'= new resistance

R'=(2pl)/a

R'=2R

R'=2*4=8 ohm

New resistance is 8 ohm

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short way :-

f a 4 ohm resistance wire is doubled and connected in series 4 +4 =8 ohms it will be

,or if it is connected in parallel it will be 1/4+1/4 =2 ohms

.as per the formula R =r1 +r 2 if they are connected in series,

if they are connected in parallel, 1 /R =1 /r1 +1/r2.

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related questions❤

• If a wire has a resistance of 4 ohms and is doubled by folding it, what will be its new resistance?

• A wire of resistance is doubled on itself, then what is its new resistance?

• The wire of resistance 16 ohm. It is melted and drawn into a wire of half its length. Calculate the resistance of the new wire. What is the percentage change in its resistance?

• A piece of resistance wire has a resistance of 4 ohm. Its diameter is doubled. What is its new resistance?

• A wire of resistance 16 ohms is elongated to double its length. What is the new resistance?

• A wire of length 'l' is doubled on itself. What is the new resistance?

• If a 12-ohm resistance wire is doubled by itself, what will be the new resistance?

• A wire of resistance is one ohm and is stretched to double its length. What is the new resistance?

• A uniform wire of resistance 100 ohm is melted and recast in a wire of a length double that of the original. What is the new resistance of the wire?

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hope it helps

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