The equivalent resistance between A and B for the given circuit is 20 x ohm where, R=100√3 Ω . Value of x is,

Question

The equivalent resistance between A and B for the given circuit is 20 x ohm where, R=100√3 Ω . Value of x is, <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-lzklcauxuluftdny.jpg" /> (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

From infinite series <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-lzklcauxulufm39q.jpg" /> (x R/R+x)+2 R=x x R+2 R2+2 R x=x R+x2 x2-2 R x-2 R2=0 x=(2+√4+8/2) R x=(√3+1) R (1/Re q)=(1/x)+(1/R)+(1/x) Re q=100 Ω=20 × 5 Ω

Q. The equivalent resistance between $A$ and $B$ for the given circuit is $20 x$ ohm where, $R = 1003 Ω$ . Value of $x$ is,

From infinite series

$\frac{x R}{R + x} + 2 R = x$
$x R + 2 R^{2} + 2 R x = x R + x^{2}$
$x^{2} - 2 R x - 2 R^{2} = 0$
$x = \frac{2 + 4 + 8}{2} R$
$x = (3 + 1) R$
$\frac{1}{R _{e q}} = \frac{1}{x} + \frac{1}{R} + \frac{1}{x}$
$R_{e q} = 100 Ω = 20 \times 5 Ω$

Q. The equivalent resistance between A and B for the given circuit is 20x ohm where, R=1003​Ω . Value of x is,

From infinite series R+xxR​+2R=x xR+2R2+2Rx=xR+x2 x2−2Rx−2R2=0 x=22+4+8​​R x=(3​+1)R Req​1​=x1​+R1​+x1​ Req​=100Ω=20×5Ω

Q. The equivalent resistance between $A$ and $B$ for the given circuit is $20 x$ ohm where, $R = 1003 Ω$ . Value of $x$ is,

From infinite series

$\frac{x R}{R + x} + 2 R = x$
$x R + 2 R^{2} + 2 R x = x R + x^{2}$
$x^{2} - 2 R x - 2 R^{2} = 0$
$x = \frac{2 + 4 + 8}{2} R$
$x = (3 + 1) R$
$\frac{1}{R _{e q}} = \frac{1}{x} + \frac{1}{R} + \frac{1}{x}$
$R_{e q} = 100 Ω = 20 \times 5 Ω$