Question

Six equal resistance of 1ohm each are connected to form the side of hexagon ABCDEF calculate the resistance offered by the combination if current enters at A and leaves at D?

Answer 1

Here 3 resistances are in series- like this two combinations of 3 resistances in series are in parallel.
So 3ohms parallel to 3 ohms
= $\frac {1}{3} + \frac{1}{3} = \frac {2}{3}$

So effective resistance is 3÷2=1.5ohms

Answer 2

Answer:

1.5Ω

Explanation:

Parallel resistance

The total current flowing through the circuit is the sum of the currents flowing through each of its branches. The circuit's two points continue to have the same potential difference across them. The sum of the reciprocals of each resistance makes up the circuit's equivalent resistance.

Figure makes it evident that there are two parallel sets of resistances between points A and D.

There are three 1-euro resistances in a row for each group. comparable resistance R1 of a single group

(AB, BC and CD) = 1Ω + 1Ω + 1Ω = 3Ω

Similar to that, the other group's comparable resistance R2

(AF, FE, ED) = 1Ω + 1Ω + 1Ω = 3Ω

Here the two parts are in parallel so by using the formula we can write,

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R2} \\=\frac{1}{3}+\frac{1}{3}\\ =\frac{2}{3}\\R=\frac{3}{2}$

Thus equivalent resistance is $\frac{2}{3}$ Ω= 1.5Ω

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