A wire of resistance 10 ohm is bent in the form of a closed circle. What is the effective resistance between the two points at the ends of any diameter of the circle?
Answers
Answer:2.5ohm
Explanation:
R=ρlA
Let us first find the values of R1 and R2. For this will use the formula for resistance of a conducting wire, i.e. R=ρlA ,
where ρ is the resistivity of the material of the wire, l is the length and A is the cross sectional area of the wire.
It is given that the resistance of the wire is 10 ohm.
⇒ρlA=10 …. (i)
Since the two resistances are of the same wire, ρ is the same for both the sections of the wire.
Let us assume that the wire has a uniform cross section. Therefore, the cross section area of both the sections will be equal. Since we have divided the circle across the diameter, the length of the two sections will be l2.
Therefore,
⇒R1=ρ(l2)A=12(ρlA) …. (ii).
And
R2=ρ(l2)A=12(ρlA) …. (iii).
From (i), (ii) and (iii) we get that R1=R2=102=5ohm.
This means that the circuit has two resistances of 5 ohms connected in parallel connection.
When two resistances R1 and R2 are in parallel connected, the effective resistance of the circuit is given as 1Reff=1R1+1R2 …. (iv),
where Reff is the effective resistance.
Substitute the values of R1 and R2 in (iv).
⇒1Reff=15+15=25
∴Reff=52=2.5ohm.
Explanation:
Therefore, the effective resistance between the two points at the end of any diameter of the circle is $2.5ohm$. Hence, the correct option is C.