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

Two uniform wires $A$ and $B$ are of the same metal and have equal masses. The radius of wire $A$ is twice that of wire $B$. The total resistance of $A$ and $B$ when connected in parallel is

$A$ uniform metallic wire has a resistance of $18\,\Omega$ and is bent into an equilateral triangle. Then,the resistance between any two vertices of the triangle is .................. $\Omega$.

Write the differences between series and parallel connections of resistors.

Two wires with temperature coefficients of resistance $\alpha_1$ and $\alpha_2$ have resistances $R_1$ and $R_2$ at $0^{\circ}C$. If they are connected in series,what is the effective temperature coefficient of resistance?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module