The ratio of the equivalent resistance of the network (shown in figure) between the points a and b when switch is open and switch is closed is x: 8. The value of x is

Question

The ratio of the equivalent resistance of the network (shown in figure) between the points a and b when switch is open and switch is closed is x: 8. The value of x is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

R eq text open =(3 R /2) R eq text closed =2 × ( R × 2 R /3 R )=(4 R /3) ( R eq text open / R eq text closed )=(3 R /2) × (3/4 R )=(9/8) ∴ x =9

Q. The ratio of the equivalent resistance of the network (shown in figure) between the points a and $b$ when switch is open and switch is closed is $x : 8$ . The value of $x$ is ____

$R_{e q open} = \frac{3 R}{2}$
$R_{e q closed} = 2 \times \frac{R \times 2 R}{3 R} = \frac{4 R}{3}$
$\frac{R _{e q open}}{R _{e q closed}} = \frac{3 R}{2} \times \frac{3}{4 R} = \frac{9}{8}$
$∴ x = 9$

Q. The ratio of the equivalent resistance of the network (shown in figure) between the points a and b when switch is open and switch is closed is x:8. The value of x is ____

Req open ​=23R​ Req closed ​=2×3RR×2R​=34R​ Req closed ​Req open ​​=23R​×4R3​=89​ ∴x=9

Q. The ratio of the equivalent resistance of the network (shown in figure) between the points a and $b$ when switch is open and switch is closed is $x : 8$ . The value of $x$ is ____

$R_{e q open} = \frac{3 R}{2}$
$R_{e q closed} = 2 \times \frac{R \times 2 R}{3 R} = \frac{4 R}{3}$
$\frac{R _{e q open}}{R _{e q closed}} = \frac{3 R}{2} \times \frac{3}{4 R} = \frac{9}{8}$
$∴ x = 9$