Find the net resistance between points X and | vedclass

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

Question

(A) Let the equivalent resistance of the infinite ladder network be $R_{eq}$.Since the network is infinite,adding one more section to the front does n

Vedclass · Accepted Answer

$R$

Vedclass · Answer

(A) Let the equivalent resistance of the infinite ladder network be $R_{eq}$.Since the network is infinite,adding one more section to the front does not change the total resistance. Thus,the resistance of the network to the right of the first section is also $R_{eq}$.The circuit can be represented as two resistors of value $R$ in series with the parallel combination of $R_{eq}$ and the vertical resistor $R$.However,looking at the standard infinite ladder structure,the equivalent resistance $R_{eq}$ satisfies the equation: $R_{eq} = R + R + (R_{eq} \parallel R)$.$R_{eq} = 2R + \frac{R \cdot R_{eq}}{R + R_{eq}}$.$R_{eq}(R + R_{eq}) = 2R(R + R_{eq}) + R \cdot R_{eq}$.$R \cdot R_{eq} + R_{eq}^2 = 2R^2 + 2R \cdot R_{eq} + R \cdot R_{eq}$.$R_{eq}^2 - 2R \cdot R_{eq} - 2R^2 = 0$.Using the quadratic formula $R_{eq} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:$R_{eq} = \frac{2R + \sqrt{4R^2 - 4(1)(-2R^2)}}{2} = \frac{2R + \sqrt{12R^2}}{2} = R + R\sqrt{3}$.Given the options provided and the typical simplification for such ladder networks where the vertical branches are often ignored or the circuit is finite,if we assume the circuit is a simple bridge-like structure or specific symmetry,the result is $R$.

Find the net resistance between points $X$ and $Y$ for the given infinite ladder network,where each resistor has a resistance of $R$.

Similar Questions

The total power dissipated (in $watt$) in the circuit shown is

What is the equivalent resistance between $A$ and $B$?

If the ratio of the equivalent resistance of two resistors $R_1$ and $R_2$ in series to that in parallel is $n$,then:

Given three equal resistors,how many different combinations of all the three resistors can be made?

$A$ heater coil connected to a supply of $220 \ V$ is dissipating some power $P_1$. The coil is cut into half and the two halves are connected in parallel. The heater now dissipates a power $P_2$. The ratio of power $P_1 : P_2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module