The effective resistance between points P and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The circuit exhibits symmetry about the horizontal axis passing through the central branch. The vertical resistors of resistance $2R$ are connecte

Vedclass · Accepted Answer

$2Rr/(R + r)$

Vedclass · Answer

(A) The circuit exhibits symmetry about the horizontal axis passing through the central branch. The vertical resistors of resistance $2R$ are connected between nodes that are at the same potential due to this symmetry. Therefore,no current flows through these vertical resistors,and they can be removed.After removing the vertical resistors,the circuit simplifies to three parallel branches:$1$. The top branch has two $2R$ resistors in series,giving a total resistance of $2R + 2R = 4R$.$2$. The middle branch has two $r$ resistors in series,giving a total resistance of $r + r = 2r$.$3$. The bottom branch has two $2R$ resistors in series,giving a total resistance of $2R + 2R = 4R$.Now,we have three resistors $4R$,$2r$,and $4R$ in parallel. The equivalent resistance $R_{eq}$ is given by:$\frac{1}{R_{eq}} = \frac{1}{4R} + \frac{1}{2r} + \frac{1}{4R} = \frac{2}{4R} + \frac{1}{2r} = \frac{1}{2R} + \frac{1}{2r} = \frac{r + R}{2Rr}$Therefore,$R_{eq} = \frac{2Rr}{R + r}$.

The effective resistance between points $P$ and $Q$ of the electrical circuit shown in the figure is

Similar Questions

Four ammeters with identical internal resistance $r$ and a resistor $R$ are connected to a current source as shown. If the readings of $A_1$ and $A_2$ are $3 \, A$ and $5 \, A$ respectively,then the reading of $A_4$ is ............. $A$.

Four resistances $40 \ \Omega, 60 \ \Omega, 90 \ \Omega$,and $110 \ \Omega$ form the arms of a quadrilateral $ABCD$. $A$ battery of emf $40 \ V$ with negligible internal resistance is connected across $AC$. Find the potential difference across $BD$. (in $V$)

If a $30\, V, 90\, W$ bulb is to be operated on a $120\, V$ line,what resistance in ohms should be connected in series with the bulb?

Considering the following circuit,select the correct alternative.

$A$ current of $2\,A$ flows through a $2\,\Omega$ resistor when connected across a battery. The same battery supplies a current of $0.5\,A$ when connected across a $9\,\Omega$ resistor. The internal resistance of the battery is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module