Three equal-resistance resistors are linked in parallel and then in series. What will the equivalent resistance ratio be when used in series and parallel?

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1:9

1:3

3:1

9:1

answer is D.

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Detailed Solution

Resistance: The hindrance placed in the way of the current's flow is referred to as resistance. R stands for it.

Resistances in series are two or more resistances connected one after another such that the same current passes through them.

In a series combination, the comparable resistance is going to be: $R_{s e r} = R_{1} + R_{2} + R_{3}$

Resistances are referred to as being in parallel when their terminals are connected at the same two places and there is an equal potential difference between them.

The formula for the net resistance/equivalent resistance(R) of parallel resistances is:

$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$
Given that,
$R_{1} = R_{2} = R_{3} = R$
The equivalent resistance of two resistors linked in series is $R_{ser} = R_{1} + R_{2} + R_{3} = R + R + R = 3 R - (1)$

The equivalent resistance of a resistor linked in parallel is
$\frac{1}{R_{para}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{2}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{3}{R}$
$∴ R_{para} = R / 3 - (2)$
Divide equations 1 and 2, we get 9:1.