Define 1 ohm resistance. A student has a resistance wire of 1 ohm. If the length of this wire is 50cm,to what length he should stretch it uniformly so as to obtain a wire of 4 ohm resistance? Justify
Answers
1 ohm is defined as the resistance of a conductor through which a current of one ampere flows when a potential difference of one volt is applied to it.
Given,
Resistance R1 = 1 Ω
Resistance R2 = 4 Ω
Length L1 = 50 cm
= 50/100 m
Legth L2 = 1/2 m
To find,
Length L2
Solution,
The length a student should stretch uniformly so as to obtain a wire of 4 Ω resistance is 2m.
We can simply find the length L2 by using the relation,
R = ρl/A
From the above relation, we get
R ∝ L
R1/L1 = R2/L2
1/1/2 = 4/L2
L2 = 4/2
L2 = 2 m
Hence, the length a student should stretch uniformly so as to obtain a wire of 4 Ω resistance is 2m.
Answer:
Explanation:
R1=1=row x L/a Volume=constant=L x a=L' x a'
R2=4=row x L'/a' ⇒L/L'=a'/a
now, ⇒50/L'=a'/a
R1/R2=L x a' / L' x a
⇒1/4=L/L' x a'/a
⇒1/4=50/L' x 50/L' (since a'/a=50/L')
⇒(L')²=50 x 50 x 4
⇒L'=√10000
⇒L'=100
Ans) The new Length is 100cm=1m