Question

how do you arrange three equal resistors each of 2ohm to obtain equivalent resistance of 3ohm
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Answer 1

Explanation:

ANSWER:-

The combination applicable are :-

• All Parallel
• All series.
• Parallel and series ( In 2:1 and vice versa)

So, checking with first criterion:-

Taking Equivalent Resistance AS x,

$\dfrac{1}{x} = \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2}$

$\dfrac{1}{x} = \dfrac{3}{2}$

$x = \dfrac{2}{3}$

So, It does not satisfy.

With all Series,

2+2+2 = 6 ohm, again not satisfied .

With Two Parallel and one series:-

$\dfrac{1}{2} + \dfrac{1}{2} = \dfrac{1}{P1}$

Parallel makes 1 ohm.

Adding it with 2 , we get

1+2 = 3 ohm.

So, 2 Parallel and one Series combination is the suitable pair.

Note:-

• In parallel connections, the equivalent resistance reduces.
• It allows appliances to work independently.
• In series combination the equivalent resistance increases.
• It does not allow appliances to work independently. Hence if one does not work, IT affects the whole circuit.