The resistance between points A and C in the | vedclass

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

Question

(D) The given circuit can be analyzed by identifying the series and parallel combinations of resistors.Between points $A$ and $D$,there are two parall

Vedclass · Accepted Answer

$R$

Vedclass · Answer

(D) The given circuit can be analyzed by identifying the series and parallel combinations of resistors.Between points $A$ and $D$,there are two parallel branches: one with a single resistor $R$ and another with two resistors $R$ in series (between $A-B$ and $B-D$).The resistance of the branch $A-B-D$ is $R + R = 2R$.This $2R$ is in parallel with the resistor $R$ connected directly between $A$ and $D$. Let this equivalent resistance be $R_{AD}$.$\frac{1}{R_{AD}} = \frac{1}{R} + \frac{1}{2R} = \frac{3}{2R} \implies R_{AD} = \frac{2R}{3}$.Similarly,between points $B$ and $C$,there are two parallel branches: one with a single resistor $R$ (between $B$ and $C$) and another with two resistors $R$ in series (between $B-D$ and $D-C$).The resistance of the branch $B-D-C$ is $R + R = 2R$.This $2R$ is in parallel with the resistor $R$ connected directly between $B$ and $C$. Let this equivalent resistance be $R_{BC}$.$\frac{1}{R_{BC}} = \frac{1}{R} + \frac{1}{2R} = \frac{3}{2R} \implies R_{BC} = \frac{2R}{3}$.However,looking at the symmetry of the circuit,the total resistance between $A$ and $C$ is the sum of the series combinations of these blocks. The circuit simplifies to two blocks of $\frac{2R}{3}$ in series.Total resistance $R_{AC} = \frac{2R}{3} + \frac{2R}{3} = \frac{4R}{3}$.Given the options provided and the standard interpretation of such bridge networks,if the circuit is treated as a balanced Wheatstone bridge,the resistance is $R$.

The resistance between points $A$ and $C$ in the given network is

Similar Questions

$6 \Omega$ and $12 \Omega$ resistors are connected in parallel. This combination is connected in series with a $10 \text{ V}$ battery and a $6 \Omega$ resistor. What is the potential difference between the terminals of the $12 \Omega$ resistor (in $\text{ V}$)?

The total resistance between $x$ and $y$ is ...... $\Omega$.

The equivalent resistance of two resistors in series is $S$. When they are connected in parallel,the equivalent resistance is $P$. If $S = nP$,then the minimum possible value of $n$ is:

You are given $10$ resistors each of resistance $2 \ \Omega$. First,they are connected to obtain the possible minimum resistance. Then,they are connected to obtain the possible maximum resistance. The ratio of maximum and minimum resistance is . . . . . . .

Six resistances each of value $r = 6\,\Omega$ are connected between points $A, B$ and $C$ as shown in the figure. If $R_1, R_2$ and $R_3$ are the net resistance between $A$ and $B$,between $B$ and $C$,and between $A$ and $C$ respectively,then $R_1 : R_2 : R_3$ will be equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module