Question

You are given 3 resistors each of 6 ohm. How will you connect them do that the combination of the resistors is 4 ohm ​

Answer 1

Attachment of the solution

$\mathtt{\huge{\underline{\red{Correct \:Question\:?}}}}$

▶ Using 3 resistors each of 6 ohm, connect them in such a way the resistors gave 4 ohm resistance .

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➡ Connect 2 in series each 6 ohms & this with other 6 ohm in parallel.

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Given :-

• Three resistors each of 6 ohm.

To Find :-

• The combination of the resistors giving resistance 4 ohm .

Calculation :-

♖ The resistance of a conductor is the property by virtue of which it opposes flow of charge through it.

♕ Series :- If a number of resistances are connected end to end so that the same current flows through each one of them in succession, then they are said to be connected in series.

♕ Parallel :- If a number of resistances are connected in between two common point so that each of them provides a a separate path for current, then they are said to be connected in parallel.

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According to question,

I drawn a diagram (refers to the attachment Fig,1) by the diagram

The total resistance in my combination,

Firstly taking the connection of series for R2 & R3

R (series) = R2 + R3

➝ (6 + 6)Ω

➝R = 12 Ω

Now we get a combination as figure 2.

➝ $\dfrac{1}{Ŕ} = \dfrac{1}{R1} + \dfrac{1}{R}$

➝ $\dfrac{1}{Ŕ} = \dfrac{1}{12} + \dfrac{1}{6}$

➝ $\dfrac{1}{Ŕ} = \dfrac{1 + 2}{12}$

➝ $\dfrac{1}{Ŕ} = \cancel{\dfrac{3}{12}}$

➝ $\dfrac{1}{Ŕ} = \dfrac{1}{4}$

➝ Ŕ = 4 Ω

➡ So, We the resistance of 4 Ω.

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