The lengths of four conducting wires are in the ratio 1:2:3:4. All wires are of same material and same radius. if they are connected in parallel with a battery .then the ratio of currents in these wires will be :
Answers
Answer:
The ratio of the lengths of 4 conducting wires, L₁:L₂:L₃:L₄ = 1:2:3:4 …… (i)
All the wires are of same material and same radius i.e., r₁=r₂=r₃=r₄…… (ii)
Let the current across each wire be “I₁”, “I₂”, “I₃” & “I₄” respectively.
The wires are connected in parallel with a battery, therefore, according to the current divider rule as the voltage is same in parallel connection, so we can write,
Current (I) = 1 / Resistance(R)
⇒ I = radius(r) / length(L) ….. (iii)
Therefore, from (iii), we get
I₁ : I₂ : I₃ : I₄
= r₁/L₁ : r₂/L₂ : r₃/L₃ : r₄/L₄
= 1/L₁ : 1/L₂ : 1/L₃ : 1/L₄ ……. [since radius is same as from (ii)]
= 1 : ½ : 1/3 : ¼
On multiplying throughout by 12 (LCM of 2, 3 & 4)
= 12 : 6 : 4 : 3
Thus, the ratio of currents in the 4 conducting wires, I₁ : I₂ : I₃ : I₄ is 12 : 6 : 4 : 3.
Answer:
12:6:4:3
Explanation: