An infinite ladder network of resistors is sh | vedclass

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

Question

(C) Let the equivalent resistance of the infinite network be $R$. Since the network is infinite,adding one more section of the same resistors will not

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Let the equivalent resistance of the infinite network be $R$. Since the network is infinite,adding one more section of the same resistors will not change the equivalent resistance.The circuit can be viewed as $R_1$ in series with the parallel combination of $R_2$ and the equivalent resistance $R$.Therefore,the equivalent resistance $R$ is given by:$R = R_1 + \frac{R \cdot R_2}{R + R_2}$Substituting the given values $R_1 = 1 \, \Omega$ and $R_2 = 2 \, \Omega$:$R = 1 + \frac{2R}{R + 2}$$R = \frac{R + 2 + 2R}{R + 2}$$R(R + 2) = 3R + 2$$R^2 + 2R = 3R + 2$$R^2 - R - 2 = 0$$(R - 2)(R + 1) = 0$Since resistance cannot be negative,we have $R = 2 \, \Omega$.

An infinite ladder network of resistors is shown in the figure. If $R_1 = 1 \, \Omega$ and $R_2 = 2 \, \Omega$,then the equivalent resistance between $A$ and $B$ is ................ $\Omega$.

Similar Questions

The dimensions of $RC$ are ($C$ and $R$ represent capacitance and resistance respectively).

Calculate the voltage across $AB$ terminals in the given circuit.

$A$ cell of negligible internal resistance and $e.m.f.$ $2 \ V$ is connected to a series combination of $2 \ \Omega$,$3 \ \Omega$,and $5 \ \Omega$ resistors. The potential difference in volts between the terminals of the $3 \ \Omega$ resistor is:

Find the $emf$ $(E)$ of the cell in $V$ required to light the bulb rated $4.5 \, W, 1.5 \, V$ fully,as shown in the circuit.

Two batteries of e.m.f. $4\,V$ and $8\,V$ with internal resistances $1\,\Omega$ and $2\,\Omega$ are connected in a circuit with a resistance of $9\,\Omega$ as shown in the figure. The current and potential difference between the points $P$ and $Q$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module