Find the equivalent resistance of the circuit

CONCEPT:

Resistance: The obstruction offered to the flow of current is known as the resistance. It is denoted by R.

• When two or more resistances are connected one after another such that the same current flows through them then it is called resistances in series.

The equivalent resistance in series combination is will be

R_ser = R₁ + R₂ 

When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal then it is called resistances in parallel.

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:

In the above figure, 6Ω and 6Ω are connected in parallel.

The net resistance/equivalent resistance(R) of two 6Ω resistances connected in parallel is given by:

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

\(\Rightarrow \frac{1}{{R'}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}\)

R’ = 3 Ω

Now R’ and 3 Ω are in series,

∴ R_net = R’ + 3 Ω

⇒ R_net = 3 Ω + 3 Ω = 6 Ω