In the circuit shown in figure, the total resistance between points X and Y is R0. The value of resistance R is

Question

In the circuit shown in figure, the total resistance between points X and Y is R0. The value of resistance R is (A) R0 (B) (R0/√3) (C) (R0/2) (D) √3 R0

Tardigrade Admin · Accepted Answer

RX Y=R+(R(R+R0)/R+(R+R0)) ⇒ R0=(2 R2+R0 R+R2+R R0/(2 R+R0)) or 2 R R0+R02=3 R2+2 R R0 ⇒ R=(R0/√3)

Q. In the circuit shown in figure, the total resistance between points $X$ and $Y$ is $R_{0}$ . The value of resistance $R$ is

$R_{0}$

$\frac{R _{0}}{3}$

$\frac{R _{0}}{2}$

$3 R_{0}$

$R_{X Y} = R + \frac{R ( R + R _{0} )}{R + ( R + R _{0} )}$
$\Rightarrow R_{0} = \frac{2 R ^{2} + R _{0} R + R ^{2} + R R _{0}}{( 2 R + R _{0} )}$
or $2 R R_{0} + R_{0}^{2} = 3 R^{2} + 2 R R_{0}$
$\Rightarrow R = \frac{R _{0}}{3}$

Q. In the circuit shown in figure, the total resistance between points X and Y is R0​. The value of resistance R is

R0​

3​R0​​

2R0​​

3​R0​