Two wires of same metal have same length, but area of cross sections are in the ratio 3 : 1 . They are in parallel. If the resistance of thin wire is 30ohm, then the total resistance of the combination will be
A) 2.5 ohm
B) 7.5 ohm
C) 5.5 ohm
D) 11 ohm
Answers
Answer:
R = 7.5 ohm
Explanation:
Let us first write the formula for resistance
R = p L / A
It means that area is resistance is inversely proportional to area
R1 / R2 = A2 / A1
30 / R2 = 1 / 3
R2 = 10 ohm
Using the parallel combination resistance formula
R = 30 x 10 / (30 + 10)
R = 7.5 ohm
The total resistance of the combination is B) 7.5 ohm
Explanation:
From question, the resistors are in parallel combination.
R = R₁R₂/(R₁ + R₂)
The resistance of one wire is given as:
R₁ = ρL/A₁ → (equation 1)
The resistance of another wire is given as:
R₂ = ρL/A₂ → (equation 2)
On dividing equation (1) and (2), we get,
R₁/R₂ = (ρL/A₁)/(ρL/A₂)
R₁/R₂ = A₂/A₁
Now, on substituting the value of area of cross section, we get,
R₁/R₂ = 1/3
∴ R₂ = 3R₁
From question on substituting the resistance of thin wire, R₂ = 30 Ω, we get,
30 = 3R₁
∴ R₁ = 10 Ω
Now, the total resistance is given as:
R = (30 × 10)/(30 + 10)
R = (300)/(40)
∴ R = 7.5 Ω