There are n resistors having equal value of resistance r. First they are connected in such a way

step 1 according to this question we know that minimum value is obtained when in parallel connection an

There are n resistors having equal value of resistance r....

There are n resistors having equal value of resistance $\mathrm{r}$. First they are connected in such a way that the possible minimum value of resistance is obtained. Then they are connected in such a way that possible maximum value of resistance is obtained the ratio of minimum and maximum values of resistances obtained in these way is.... (A) $(1 / n)$ (B) $\mathrm{n}$ (C) $\mathrm{n}^{2}$ (D) $\left(1 / \mathrm{n}^{2}\right)$

There are n resistors having equal value of resistance $\mathrm{r}$. First they are connected in such a way that the possible minimum value of resistance is obtained. Then they are connected in such a way that possible maximum value of resistance is obtained the ratio of minimum and maximum values of resistances obtained in these way is....
(A) $(1 / n)$
(B) $\mathrm{n}$
(C) $\mathrm{n}^{2}$
(D) $\left(1 / \mathrm{n}^{2}\right)$

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Key Concepts

Parallel Connection

In a parallel connection, the components are connected across the same two nodes, giving multiple paths for the current. The equivalent resistance is calculated using the reciprocal formula, leading to a value that is lower than any individual resistor's resistance. This creates conditions for the minimum total resistance in a circuit of resistors.

Series Connection

In a series connection, electrical components are connected end-to-end, so the same current flows through each component. The total resistance of the circuit is simply the sum of the individual resistances, which results in the maximum equivalent resistance when resistors are connected one after another.

Equivalent Resistance

Equivalent resistance is the value of a single resistor that can replace a network of resistors without changing the overall current or voltage characteristics of the circuit. It is computed differently depending on whether resistors are in series (simple summation) or in parallel (using the reciprocal sum), and provides a simplified analysis of the circuit performance.

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