Question

Two wires that are made up of same material have length in ratio 4:3 and area of cross- section in ratio 5:4. When wires are connected in parallel across a voltage source, the ratio of current flowing through them is

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Answer 1

Given :

Ratio of lengths = 4:3

Ratio of area of cross sections = 5:4

Both wires are made up of same material.

To Find :

Ratio of current flow through them when they are connected in parallel across voltage source.

Solution :

❖ We know that, resistance of a conductor is directly proportional to the length of conductor and inversely proportional to the area of cross section.

Mathematically, R ∝ L/A

By putting proportionality constant;

• R = ρ × L/A

Where ρ denotes resistivity of conductor.

Here both wires are made up of same material it means both wires have same resistivity.

❖ In parallel connection, voltage across each resistor is same.

We know that, I = V/R

$\sf:\implies\:\dfrac{I_1}{I_2}=\dfrac{V}{R_1}\times \dfrac{R_2}{V}$

$\sf:\implies\:\dfrac{I_1}{I_2}=\dfrac{R_2}{R_1}$

$\sf:\implies\:\dfrac{I_1}{I_2}=\dfrac{L_2}{L_1}\times\dfrac{A_1}{A_2}$

$\sf:\implies\:\dfrac{I_1}{I_2}=\dfrac{3}{4}\times\dfrac{5}{4}$

$\sf:\implies\:\dfrac{I_1}{I_2}=\dfrac{15}{16}$

$:\implies\:\underline{\boxed{\bf{\purple{I_1:I_2=15:16}}}}$

Answer 2

Explanation:

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