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
JEE
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
A $50\,V$ battery is connected across a $10\, ohm$ resistor. The current is $4.5\, amperes$. The internal resistance of the battery is ............. $ohm$
View Solution
2
The mechanism of the heat produced in a conductor when an electric current flows through it, can be explained on the basis of
View Solution
3
Find current through the branch $ad$ of the circuit shown in figure. :-............. $A$
View Solution
4
Assume a hypothetical wire in which free electron density changes with temperature in proportionality $n\ \alpha \ T$ assuming $\tau $(Relaxation time of collision) and dimensions of wire remain unchanged with increasing temperature. Which one of the resistance $v/s$ temperature graph is true
View Solution
5
Find potential difference between $A$ and $B$ in given circuit in steady state ............... $\mathrm{V}$
View Solution
6
Two long coaxial and conducting cylinders of radius $a$ and $b$ are separated by a material of conductivity $\sigma$ and a constant potential difference $V$ is maintained between them, by a battery. Then the current, per unit length of the cylinder flowing from one cylinder to the other is -
View Solution
7
When two resistance $R_1$ and $R_2$ connected in series and introduced into the left gap of a meter bridge and a resistance of $10 \Omega$ is introduced into the right gap, a null point is found at $60 cm$ from left side. When $R_1$ and $R_2$ are connected in parallel and introduced into the left gap, a resistance of $3 \Omega$ is introduced into the right-gap to get null point at 40 cm from left end. The product of $R_1 R_2$ is $.............\Omega$
View Solution
8
According to Joule's law, if the potential difference across a conductor having a material of specific resistance remains constant, then the heat produced in the conductor is directly proportional to
View Solution
9
The internal resistance of a primary cell is $4\, ohm$. It generates a current of $0.2\, amp$ in an external resistance of $21\, ohm$. The rate at which chemical energy is consumed in providing the current is .............. $J/s$
View Solution
10
A source of $e.m.f.$ $E = 15\,V$ and having negligible internal resistance is connected to a variable resistance so that the current in the circuit increases with time as $i = 1.2 t + 3$. Then, the total charge that will flow in first five second will be ............... $C$
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free