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(D) The equivalent resistance of the group of resistances is $R$.Case $1$: When a resistance $r$ is connected in parallel to the group,the new equival

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Both $(B)$ and $(C)$

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(D) The equivalent resistance of the group of resistances is $R$.Case $1$: When a resistance $r$ is connected in parallel to the group,the new equivalent resistance $R_1$ is given by the formula:$R_1 = \frac{R \cdot r}{R + r}$Since $\frac{r}{R + r} Case $2$: When a resistance $r$ is connected in series to the group,the new equivalent resistance $R_2$ is given by:$R_2 = R + r$Since $r > 0$,it follows that $R_2 > R$.Therefore,both statements $R_1  R$ are correct. Thus,option $(D)$ is the correct answer.

The equivalent resistance of a group of resistances is $R$. If another resistance is connected in parallel to the group,its new equivalent becomes $R_1$,and if it is connected in series to the group,its new equivalent becomes $R_2$. We have:

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