Answer:
The ratio of the ratio of series and parallel combination is n²:1.
Explanation:
The equivalent resistance in case of series combination is given by :
[tex]R_s=R_1+R_2+.....+R_n=nR[/tex] ....(1)
The equivalent resistance in case of parallel combination is given by :
[tex]R_P=\dfrac{1}{R_1}+\dfrac{1}{R_2}+.....+\dfrac{1}{R_n}=\dfrac{R}{n}[/tex] ....(2)
Dividing equation (1) and (2) we get :
[tex]\dfrac{R_s}{R_P}=\dfrac{nR}{R/n}\\\\\dfrac{R_s}{R_P}=\dfrac{n^2}{1}\\\\R_s:R_P=n^2:1[/tex]
So, the ratio of the ratio of series and parallel combination is n²:1. Hence, this is the required solution.
n resistance is each of resistance R is first connected in series and then in parallel , the ratio of series and parallel combination will be [tex]n^{2}[/tex] : 1
In a series combination, the resistances are connected with end to end in contact, such that current flow is equal in all the resistances in the combination. Whereas in the parallel combination, resistances are connected in such a manner that they get an equal voltage across their ends.
Parallel combination. When two or more resistances are connected between the same two points, they are said to be connected in parallel combination. The reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the sum of the reciprocals of all the individual resistances.
if n number of resistances are connected in series combination .
R (equivalent ) = R1 + R2 + R3 + R4 -------- + Rn
= R + R + R + R ---------------- + R
= n*R
if n number of resistances are connected in parallel combination .
1/ R (equivalent ) = 1/R1 + 1/R2 + 1/R3 ---------------- 1/Rn
= 1/R + 1/R + 1/R + --------------------- 1/R
= n/R
R (equivalent ) = R/n
Ration = series combination / parallel combination
= n*R / (R/n) = [tex]n^{2}[/tex] /1
= [tex]n^{2}[/tex] : 1
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