Show that the ratio series
connection to the parallel connection of 'n' nos. of resistance is of value 'R' ohm is n2:1?
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2
Answer:
First of all, consider a circuit where "n" resistors are connected in series.
In that case, the net resistance is
= R+R+R+....... n times
= nR
Now consider a circuit where "n" resistors are connected in parallel with one another.
In that case the resistance is given by
1/R eq.= 1/R + 1/R + 1/R +........ n times
R eq. = R/n.
Now the required ratio of series to parallel combinations
= (nR)/ (R/n)
= n^2 : 1
Hence proved.
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