Find out currents?

Asked by ravi01.ch 26th June 2018, 1:32 PM

Answered by Expert

Answer:

For example let us take a hexagon and assume all the sides has equal resistance as shown in figure.

If two resistances R1 and R2 are connected in parallel, then the equivalenet resistance is less than any of the resistances R1 and R2.

Using this concept, let us have a parallel combination of resitance of one side and the resistances of all other side as shown in figure.

In the figure, parallel combination is made using resistance of side AB and resistances of all oother sides put together.

We are trying to find equivalent resistance across points A and B.

in this example we have n-sided polygon so that n = 6 ( n is even number )

minimum equivalent resistance =

begin mathsize 12px style fraction numerator R cross times left parenthesis n minus 1 right parenthesis R over denominator open square brackets R plus open parentheses n minus 1 close parentheses R close square brackets end fraction space equals space fraction numerator open parentheses n minus 1 close parentheses over denominator n end fraction R end style

To get maximum resitance using parallel combination, the sides are divided into two half . This is done for hexagon as shown in right side of figure, by finding equivalent resitance across points C and F

maximum equivalent resistance

begin mathsize 12px style equals space fraction numerator begin display style n over 2 end style R space cross times begin display style n over 2 end style R over denominator open parentheses begin display style n over 2 end style R space plus space begin display style n over 2 end style R close parentheses end fraction space equals space fraction numerator n space over denominator 4 end fraction R end style

But neither minimum or maximum matches with the list of answers. But I believe this procdure is correct one to get minimum or maximum value of equivalent resistance for n-sided polygon ( n is even)

Answered by Expert 26th June 2018, 5:56 PM

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