Question

A finite square grid, each link having resistance $r$, is fitted in a resistance-less conducting circular wire. Determine the equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ (in $\Omega$ ) if $\text{r}=(\dfrac{80}{7})\Omega $

Answer 1

Hint: The equivalent resistance is where either parallel or series-connected aggregate resistance is calculated. Basically, either in series or parallel, the circuit is designed. When you move the charges/current through your devices, electrical resistance shows how much energy one needs. Calculate The resultant resistance between A to B.

Complete answer:
For each type of circuit, the method we use for calculating equivalent resistance is different. For a series circuit, the resistances of each element are simply added up. However, in a parallel circuit, the total reciprocal resistance is equal to the sum of each branch's reciprocal resistance. Basically, either in series or parallel, the circuit is designed. When you move the charges/current through your devices, electrical resistance shows how much energy one needs.
If we connect battery between $\mathrm{A}$ and $\mathrm{B}$, then different points will be at the same potentials. $(1,2,3,4),(5,6,7,8),(9,10,11,12,13,14,15,16),$ and (17,18,19,20)
The resulting circuit can be:
${{\text{R}}_{\text{AB}}}=\dfrac{21}{40}\text{r}$
$\Rightarrow {{\text{R}}_{\text{AB}}}=\dfrac{21}{40}\times \dfrac{80}{7}$
$\therefore {{\text{R}}_{\text{AB}}}=6\Omega $
The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is $6\Omega $

Note:
The equivalent resistance is where either parallel or series-connected aggregate resistance is calculated. Basically, either in series or parallel, the circuit is designed. As used in electrical circuits, practical capacitors and inductors are not ideal components with only capacitance or inductance. Equivalent resistance is a purely resistive property that changes with no other variable. An additional name given to the impedance is effective resistance. A set of resistors or components that only have resistance is defined as equivalent resistance.