In the figure, the value of resistors to be connected between C and D so that the resistance of the entire circuit between A and

Q: In the figure, the value of resistors to be connected between $C$ and $D$ so that the resistance of the entire circuit between $A$ and $B$ does not change with the number of elementary sets used is

b (b) Cut the series from $XY$ and let the resistance towards right of $XY$ be ${R_0}$ whose value should be such that when connected across $AB$ does not change the entire resistance. The combination is reduced to as shown below. The resistance across $EF, = {R_{EF}} = ({R_0} + 2R)$ Thus ${R_{AB}} = \frac{{({R_0} + 2R)R}}{{{R_0} + 2R + R}} = \frac{{{R_0}R + 2{R^2}}}{{{R_0} + 3R}} = {R_0}$ $ \Rightarrow R_0^2 + 2R{R_0} - 2{R^2} + 0 \Rightarrow {R_0} = R(\sqrt 3 - 1)$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

In the figure, the value of resistors to be connected between $C$ and $D$ so that the resistance of the entire circuit between $A$ and $B$ does not change with the number of elementary sets used is

A$R$
B$R(\sqrt 3 - 1)$
C$3 R$
D$R(\sqrt 3 + 1)$

Diffcult

STD 11 Science
NEET
STD 12 - 3. current electricity
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
The $V-i$ graph for a conductor makes an angle $\theta $ with $V-$ axis. Here $ V$ denotes the voltage and $i$ denotes current. The resistance of conductor is given by
View Solution
2
In potentiometer a balance point is obtained, when
View Solution
3
Two wires $A$ and $B$ of same material and mass have their lengths in the ratio $1 : 2$. On connecting them to the same source, the rate of heat dissipation in $B$ is found to be $5\,W$. The rate of heat dissipation in $A$ is............ $W$
View Solution
4
A uniform wire of resistance $9\, ohm$ is bent in the form of a circle. The effective resistance across the points $A$ and $B$ is ............... $\Omega$
View Solution
5
In a meter bridge experiment null point is obtained at $20\, cm$ from one end of the wire when resistance $X$ is balanced against another resistance $Y$. If $X < Y$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $4X$ against $Y$ ........... $cm$
View Solution
6
In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance $P\, = 4\,\Omega $ and the neutral point $N$ is at $60\,cm$ from $A$. Now an unknown resistance $R$ is connected in series to $P$ and the new position of the neutral point is at $80\,cm$ from $A$ . The value of unknown resistance $R$ is
View Solution
7
A wire is connected to a battery between the point $M$ and $N$ as shown in the 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 the figure $(2)$. Which of the following quantities increases?
View Solution
8
A $5\;ampere$ fuse wire can withstand a maximum power of $1\; watt$ in the circuit. The resistance of the fuse wire is
View Solution
9
A potentiometer wire $AB$ having length $L$ and resistance $12\, r$ is joined to a cell $D$ of $emf$ $\varepsilon $ and internal resistance $r$. A cell $C$ having $emf$ $\varepsilon /2$ and internal resistance $3r$ is connected. The length $AJ$ at which the galvanometer as shown in figure shows no deflection is
View Solution
10
For a cell terminal $P.D.$ is $2.2\;V$ when circuit is open and reduces to $1.8\;V$ when cell is connected to a resistance of $R = 5\,\Omega $. Determine internal resistance of cell $(r)$ is then ........ $\Omega$
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free