What is the resultant resistance if two resistors of each 2 Ω resistance are connected in parallel?

CONCEPT:

• Resistances in parallel combination: When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.
  • A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together.

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The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

CALCULATION:

Given that: R₁ = R₂ = 2 Ω 

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

\(\frac{1}{R} = \frac{1}{{{2}}} + \frac{1}{{{2}}} = 2/2 = 1\)

So Resultant resistance (R) = 1 Ω 

• The resultant resistance if two 2 Ω resistors are connected in parallel is 1 Ω. So option 2 is correct.

EXTRA POINTS:

• Resistances in series combination: When two or more resistances are connected one after another such that the same current flows through them are called as resistances in series.

The net resistance/equivalent resistance (R) of resistances in series is given by:

Equivalent resistance, R = R1 + R2