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Q.

Nichrome wire of length $' l'$ and radius $' r'$ has a resistance of $10 Ω .$ How would the resistance of the wire change when only the length of the wire is doubled?

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a

Resistance becomes doubles(

20 Ω

)

b

Resistance becomes half (

5 Ω

)

c

Resistance remains the same (

10 Ω

)

d

None of the above

answer is A.

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Detailed Solution

Nichrome wire of length '

l

' and radius '

r

' has a resistance of

10 Ω

. Resistance becomes doubled (

20 Ω

) when only the length of the wire is doubled.
The resistance of a conductor is the property of the conductor due to which it resists a flow of electric charges (or current) through it. Its SI unit is the ohm, denoted by the greek letter

Ω

.
Resistance depends on the length of the wire, the area of the cross-section of the wire and the material of the wire or conductor. When the length of the wire doubles, its resistance will also double.
Mathematically;
Given that length of wire

= l

Radius

= r

Resistance

R = 10 Ω

We know that, the specific resistance formula,

\Rightarrow

R_{} = \frac{ρl}{A}

(Where

R_{}

is the resistance of wire,

l

is the length;

A

is the area of cross-section, and

ρ

is the resistivity)

\Rightarrow

R_{1} = \frac{ρ (2 l)}{A}

Here,

R_{1}

is the new resistance of the wire after doubling the length of the wire.

\Rightarrow R_{1} = 2 \frac{(ρl)}{A}

\Rightarrow R_{1} = 2 R

(since

\frac{(ρl)}{A}

= R

)

\Rightarrow R_{1} = 2 (10)

(because

R = 10

)

\Rightarrow R_{1} = 20 Ω

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Nichrome wire of length 'l' and radius 'r' has a resistance of 10 Ω. How would the resistance of the wire change when only the length of the wire is doubled?