Find equivalent resistance between A&B in the following circuit
 
A. \[\dfrac{{3R}}{2}\]
B. \[\dfrac{{2R}}{3}\]
C. \[2R\]
D. \[3R\]

Hint: The diagram depicts resistances connected in series between two spots. In a series combination, the equivalent resistance is the sum of all resistances. To add all the resistances, we utilize the sum of n terms of arithmetic progression. The sum of n terms is determined by the number of terms, the first term, and the common difference.




Formula used:
By analyzing the figure, the suitable formula for the figure is the formula for equivalent resistance in parallel.
That is,
\[\dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}}\]


Complete answer:
We have been provided a circuit in the question that,

We have been already know that the formula for the equivalent resistance in series can be written as
\[R = {R_1} + {R_2}\]
And we also know that the formula for the equivalent resistance in parallel can be written as
\[\dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}}\]
After knowing the formula, the circuit should be rearranged accordingly
So, the equivalent resistance of upper branch between the points A and B is equal to ${ \dfrac{R}{2} + R + \dfrac{R}{2} }$ = 2R

So, the equivalent resistance of upper branch and lower branch between the points A and B is equal to ${ \dfrac{1}{R_{eq}} = \dfrac{1}{2R} + \dfrac{1}{R} }$
=> ${ R_{AB} = \dfrac{2R}{3}}$


Therefore, the equivalent resistance between A&B in the given circuit is \[\dfrac{{2R}}{3}\]
Hence, the option B is correct



Note:Students should be careful in solving these types of problems. We should expect a parallel circuit to have more than two channels for current to flow through it. The total current coming from the source will be equal to the sum of the currents going via each of the pathways. In a series circuit, however, the overall resistance equals the sum of the individual resistances. Similarly, the voltage supplied in the series circuit will equal the sum of all the individual voltage decreases.