Question

Three wires are connected parallel to each other. If the ratio of current in the wires is 2 : 3 : 5 when a potential difference V is applied to this combination, then what is the ratio of their resistance:
1. 2 : 3 : 5
2. 15 : 10 : 6
3. 5 : 3 : 2
4. 6 : 10 : 15

Answer 1

Correct Answer - Option 2 : 15 : 10 : 6

CONCEPT

Ohm's law

• Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature remain constant.

​\(⇒ V=IR\)

Where V = voltage, I = current and R = resistance

CALCULATION:

Given I₁ : I₂ : I₃ = 2 : 3 : 5

So,

⇒ I₁ = 2x

⇒ I2 = 3x

⇒ I3 = 5x

• When the wires are connected parallel to each other, the potential difference will be equal for each wire.
• By ohm's law, the resistance of the wire is given as,

\(⇒ R=\frac{V}{I}\)     -----(1)

• The resistance of wire 1 is given as,

\(⇒ R_{1}=\frac{V}{I_{1}}\)

\(⇒ R_{1}=\frac{V}{2x}\)     -----(2)

• The resistance of wire 2 is given as,

\(⇒ R_{2}=\frac{V}{I_{2}}\)

\(⇒ R_{2}=\frac{V}{3x}\)     -----(3)

• The resistance of wire 3 is given as,

\(⇒ R_{3}=\frac{V}{I_{3}}\)

\(⇒ R_{3}=\frac{V}{5x}\)     -----(4)

By equation 2, equation 3, and equation 4,

⇒ R₁ : R2 : R3

\(⇒ \frac{V}{2x}:\frac{V}{3x}:\frac{V}{5x}\)

\(⇒ \frac{1}{2}:\frac{1}{3}:\frac{1}{5}\)

⇒ 15 : 10 : 6

• Hence, option 2 is correct.