Question

Find the ratio of series to parallel combination if R1=2R,R2=6R,R3=4R

Answer 1

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Answer 2

Answer:

The Ratio of series to parallel combination is 11 : 1

Explanation:

Given as :

The resistance are as follows

$R_1$  = 2 R

$R_2$  = 6 R

$R_3$  = 4 R

Let The equivalent series resistance = $R_e_q$  

For, series resistance

$R_e_q$  = $R_1$ + $R_2$ + $R_3$

$R_e_q$ = 2 R + 6 R + 4 R

∴  $R_e_q$ = 12 R              

So, The equivalent series resistance = $R_e_q$  = 12 R

Again

For parallel resistance

$\dfrac{1}{R'_e_q}$  = $\dfrac{1}{R_1}$  + $\dfrac{1}{R_2}$  + $\dfrac{1}{R_3}$

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

Or, $\dfrac{1}{R'_e_q}$  = $\dfrac{6+2+3}{12R}$

Or, $\dfrac{1}{R'_e_q}$ = $\dfrac{11}{12R}$

∴   $R'_e_q$  = $\dfrac{12R}{11}$

So, The equivalent parallel resistance = $R'_e_q$  = $\dfrac{12R}{11}$

Now,

The Ratio of series to parallel combination = $\dfrac{R_e_q}{R'_e_q}$  = $\dfrac{12R}{\dfrac{12R}{11} }$

∴ $\dfrac{R_e_q}{R'_e_q}$  = 11

So, The Ratio of series to parallel combination = 11 : 1

Hence, The Ratio of series to parallel combination is 11 : 1  Answer