Question

Four resistance of 4 ohms are connected in parallel. The resultant resistance will be :
(A) 4 ohms (B) 3 ohms
(C) 2 ohms (D) 1 ohm

Answer 1

Explanation:

see this attachment

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Answer 2

Given:

Four resistance of 4 ohms are connected in parallel.

To Find:

The resultant resistance

Solution:

When resistances are combined in parallel, the resultant resistance is given by the equation,

1/R = 1/R₁ + 1/R₂ + 1/R₃......1/Rn.........(i)

Since it is given that R₁ = R₂ = R₃ = R₄ = 4Ω

Putting the values in eq (i), we get,

1/R = 1/4 + 1/4 + 1/4 + 1/4

⇒1/R = (4/4) = 1 Ω

An alternative way to solve this is,

When equal resistances are joined in parallel, the resultant resistance,

R' = R/n.........(ii)

where n is the total number of resistances combined and R is the value of each resistance.

Putting the given values in eq (ii), we get,

R' = (4/4) = 1 Ω

Hence, the resultant resistance of the given series is 1Ω