Question

Three equal resistances are connected in series then in parallel.What will be the ratio of their equivalent resistance ?

Answer 1

The ratio is equal to 9:1


SOLUTION :-

Let the resistance of 3 resistors be 'r' ohm

Number of resistors = 3 resistor
Resistance of each resistor = r ohm

Now,

Case 1 :-

(when resistors are connected in series)

So,

Equivalent Resistance or R is equal to :-
$nr$
Where,
n is the number of resistor and r is the resistance of each resistor

Thus,
In this case :-

Equivalent Resistance is equal to 3r



Case 2 :-

(when resistors are connected in parallel)

So,
Equivalent Resistance or R' is equal to :-

$\frac{r}{n}$

So,
In this case :-

Equivalent Resistance will be equal to
$\frac{r}{3}$


Now,

Equivalent Resistance (series) = 3r ohm

Equivalent Resistance (parallel) = r/3 ohm


Ratio of the equivalent resistances is as follows :-

$\dfrac{series}{parallel} = \dfrac{3r}{ \dfrac{r}{3} } = \dfrac{9}{1} \\ \\ = 9:1$


Thanks!