Question

Find the ratio of series to parallel combination ifR1=2R, R2=6R, R3=4R.

Answer 1

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Answer 2

The ratio of series to parallel combination is 11:1

Explanation:

The series combination of resistor is given by :

$R_s=R_1+R_2+R_3$

$R_s=2R+6R+4R$

$R_s=12R$...........(1)

The parallel combination of resistor is given by :

$\dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}$

$\dfrac{1}{R_p}=\dfrac{1}{2R}+\dfrac{1}{6R}+\dfrac{1}{4R}$

$R_p=\dfrac{12R}{11}$...........(2)

Dividing equation (1) and (2) as :

$\dfrac{R_s}{R_p}=\dfrac{11}{1}$

So, the ratio of series to parallel combination is 11:1. Hence, this is the required solution.

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