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A combination consists of three resistors in series. Four similar sets are connected in parallel. If the resistance of each resistor is 2 ohm, the resistance of the combination is :(A) \[2.5\Omega \](B) \[3\Omega \](C) \[1.5\Omega \](D) \[5\Omega \]

Last updated date: 21st Sep 2024
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Hint Understand the given scenario. It is given that three 2 ohms resistors are connected in series. Using total resistance in a series circuit formula , find the overall resistance of this combination. Then it is said that it is connected in four parallel rows. Use total resistance in a parallel circuit to find the overall resistance.

It is given that there are three resistors given in series connection. This means that the current remains constant throughout whereas the potential difference between the starting node of the combination and the ending node of the combination. Thus, when two or more resistors are connected in series, the total resistance is given as the sum of all individual resistance. Mathematically,
\[{R_s} = {R_1} + {R_2} + {R_3} + ..... + {R_n}\]
In our question, it is given as three 2 ohms resistors. Thus the overall resistance in series combination is,
\[ \Rightarrow {R_s} = {R_1} + {R_2} + {R_3}\]
\[ \Rightarrow {R_s} = 6\Omega \]
Now, four of these \[6\Omega \]combination resistors are connected parallel to each other. In a parallel connection, the current varies as there is a division in its path, whereas the potential difference across the path remains constant. Thus the overall resistance of the parallel circuit is given as the sum of reciprocal values of individual resistance of the resistors. Mathematically,
\[ \Rightarrow \dfrac{1}{{{R_p}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}} + \dfrac{1}{{{R_4}}}.... + \dfrac{1}{{{R_n}}}\]
Now in our question, it is given that there four \[6\Omega \]combination resistors connected in parallel to each other.
\[ \Rightarrow \dfrac{1}{{{R_p}}} = \dfrac{1}{6} + \dfrac{1}{6} + \dfrac{1}{6} + \dfrac{1}{6}\]
\[ \Rightarrow \dfrac{1}{{{R_p}}} = \dfrac{4}{6}\]
On reciprocating on both sides, we get
\[ \Rightarrow {R_p} = \dfrac{6}{4}\]
\[ \Rightarrow {R_p} = 1.5\Omega \]
The overall value of the combination is \[1.5\Omega \]

Thus, option (c) is the right answer for the given question.

Note In a series circuit, current is said to be constant irrespective of the component because series circuits don’t have any break or nodal division in the circuit causing the current to flow in two or more directions. Thus , the current flows straight and remains constant in series circuits.