Resistance Depends on Length


 
 
Concept Explanation
 

Resistance Depends on Length

Resistance depends on the length of the wire:

The resistance of ohmic circuit elements such as metal wires or carbon resistor depends on the length of the wire. To find dependence,we will follow the following steps

1 Keep the thickness of the wire as fixed and just increase or decrease the length of the wire.

2. Apply a potential difference across the ends of the wire and calculate the value of R from the values of current and potential difference

3. Calculate the value of R for different values of the length of the wire.

4. Plot a graph as shown below by taking length along x axis and resistance along y axis

From the graph we observe that as length increases the resistance also increases. So we find that there is a proportionality between the length L of the wire and the resistance of the wire R. The resistance of a conductor R is directly proportional to its length l          

i.e.                        dpi{100} large R;alpha ;l

                             large R=k_1;l

Since, the resistance of a wire is directly proportional to its length, i.e. when the length of the wire is doubled or halved, then its resistance also gets doubled or halved.

Illustration: In a circuit  when a current of 5 A flows through a  certain wire having resistance R a potential difference of 10 V is generated across the wire. What will be the new potential difference generated across the wire if the length of the wire is doubled.

Solution:  It is given that

V= 10 V

I = 5 A

R= ?

V= IR

Rightarrow R = frac{V}{I}=frac{10}{5}= 2Omega

As the length of the wire is doubled so the resistance will be doubled.

Rightarrow R_{new} =2times 2= 4Omega

Rightarrow V_{new} =IR_{new}= 5times 4= 20 V

So new potential difference of 20V is generated across the wire if the length of the wire is doubled.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Diamond conducts heat due to  ________________

 

Right Option : B
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Explanation
Question : 2

Calculate resistance  of 10m  long copper wire of radius 1mm.(Resistivity of copper is( 1.72:X:10^{-8} Omega m)

Right Option : C
View Explanation
Explanation
Question : 3

A constant voltage is applied between the two ends of a uniform metallic wire. If both the length and radius of wire are doubled the:

Right Option : A
View Explanation
Explanation
 
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