(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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(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.

Class 12 Physics Current Electricity Equivalent Resistance - Series and Parallel , Circuit

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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:

A
$R_1 > R$
B
$R_1 < R$
C
$R_2 > R$
D
Both $(B)$ and $(C)$

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Current Electricity

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Equivalent Resistance - Series and Parallel , Circuit

If $\sigma_1$,$\sigma_2$,and $\sigma_3$ are the conductivities of three conductors,what will be their equivalent conductivity when they are connected in series?

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The power consumed when $10 \ V$ voltage is applied to a series combination of $10$ resistors of each $1 \ \Omega$ is $P_{s}$ and the power consumed when the same $10 \ V$ is applied to the parallel combination of these $10$ resistors is $P_p$. The value of $\frac{P_{s}}{P_{p}}$ is

DifficultAP EAMCET 2022

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$A$ wire is connected to a battery between the points $M$ and $N$ as shown in figure $(1)$. The same wire is bent in the form of a square and then connected to the battery between the points $M$ and $N$ as shown in figure $(2)$. Which of the following quantities increases?

Medium

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Three resistors are connected to form the sides of a triangle $ABC$. The resistances of the sides $AB$,$BC$,and $CA$ are $40\,\Omega$,$60\,\Omega$,and $100\,\Omega$ respectively. The effective resistance between the points $A$ and $B$ in $\Omega$ will be:

Medium

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In the given figure,switches $S_{1}$ and $S_{2}$ are initially open. What is the equivalent resistance across $a b$ when the switches $S_{1}$ and $S_{2}$ are closed? (in $\Omega$)

DifficultJEE MAIN 2021

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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:

Similar Questions

If $\sigma_1$,$\sigma_2$,and $\sigma_3$ are the conductivities of three conductors,what will be their equivalent conductivity when they are connected in series?

The power consumed when $10 \ V$ voltage is applied to a series combination of $10$ resistors of each $1 \ \Omega$ is $P_{s}$ and the power consumed when the same $10 \ V$ is applied to the parallel combination of these $10$ resistors is $P_p$. The value of $\frac{P_{s}}{P_{p}}$ is

$A$ wire is connected to a battery between the points $M$ and $N$ as shown in figure $(1)$. The same wire is bent in the form of a square and then connected to the battery between the points $M$ and $N$ as shown in figure $(2)$. Which of the following quantities increases?

Three resistors are connected to form the sides of a triangle $ABC$. The resistances of the sides $AB$,$BC$,and $CA$ are $40\,\Omega$,$60\,\Omega$,and $100\,\Omega$ respectively. The effective resistance between the points $A$ and $B$ in $\Omega$ will be:

In the given figure,switches $S_{1}$ and $S_{2}$ are initially open. What is the equivalent resistance across $a b$ when the switches $S_{1}$ and $S_{2}$ are closed? (in $\Omega$)

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