If the resistance of a conductor of length 5m is10 ohm, what is the resistance of a conductor of length 20 m of the same material?
Answers
Answer :-
40 Ω
Solution :-
It was experimetally proven that Resistance ( R ) is directly proportional to the length of the conducror ( l ) and inversely proportional to the cross section area ( A ).
⇒ R ∝ l/A
⇒ R = ρl/A
[ Where, ρ is a propportionality constant and is called Resistivity or Specific Resistance. ]
Coming to Question :
Given :-
Resistance ( R ) = 10 Ω
Length of the conductor ( l ) = 5
Using Resistance formula
⇒ R = ρl/A
⇒ 10 = ρ5/A
⇒ 10/5 = ρ/A
⇒ 2 = ρ/A
⇒ ρ/A = 2
If the length of the same conductor is 20
Again using Resistance formula
⇒ R = ρl/A
⇒ R = ρ * 20/A
⇒ R = 20 * ρ/A
For same material Resistivity ( ρ ) is same since its a proportionality constant.
So, therefore we can substitute ρ/A = 2 in the above equation
⇒ R = 20 * 2
⇒ R = 40 Ω
Therefore the resistance of the conductor of length 20 m is 40 Ω.
Answer:
Explanation:
Given :-
Resistance = 10 Ω
Length of the conductor = 5
To Find :-
Resistance of a conductor.
Formula to be used :-
Resistance formula i.e R = ρl/A
Solution :-
Putting all the values, we get
⇒ R = ρl/A
⇒ 10 = ρ5/A
⇒ 10/5 = ρ/A
⇒ 2 = ρ/A
⇒ ρ/A = 2
If the length of the same conductor is 20
Using Resistance formula, we get
⇒ R = ρl/A
⇒ R = ρ × 20/A
⇒ R = 20 × ρ/A
Therefore, we can substitute ρ/A = 2 in the above equation
⇒ R = 20 × 2
⇒ R = 40 Ω
Hence, the resistance of the conductor of length 20 m is 40 Ω.