Three resistors with magnitudes 2, 4 and 8 ohm are connected in parallel. The equivalent resistance of the system would be
less than 2 ohm
more than 2 ohm but less than 4 ohm
4 ohm
14 ohm
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2016
Given resistances are R₁ = 2 ohm, R₂ = 4 ohm, and R₃ = 8 ohm.
The formula for equivalent resistance in parallel is:
1/Req = 1/R₁ + 1/R₂ + 1/R₃
Substituting the values:
1/Req = 1/2 + 1/4 + 1/8
To add these fractions, find a common denominator, which is 8:
1/Req = 4/8 + 2/8 + 1/8
1/Req = (4 + 2 + 1) / 8
1/Req = 7/8
Now, take the reciprocal to find Req:
Req = 8/7 ohm
To compare this value with the options, calculate the decimal value: Req ≈ 1.14 ohm.
A key principle of parallel resistance is that the equivalent resistance is *always less than the smallest individual resistance* in the combination. In this case, the smallest resistance is 2 ohm, and 8/7 ohm (approx 1.14 ohm) is indeed less than 2 ohm.