Two known resistances of R Omega and 2R Ome | vedclass

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

Question

(A) From the circuit diagram, the resistance $2R$ and $X$ are in series. Their equivalent resistance is $R_{s} = 2R + X$.This combination is in parall

Vedclass · Accepted Answer

$(\sqrt{3}-1)R$

Vedclass · Answer

(A) From the circuit diagram, the resistance $2R$ and $X$ are in series. Their equivalent resistance is $R_{s} = 2R + X$.This combination is in parallel with the resistance $R$. The equivalent resistance $R_{eq}$ between points $A$ and $B$ is given by:$R_{eq} = \frac{R \cdot (2R + X)}{R + (2R + X)}$Given that $R_{eq} = X$, we have:$X = \frac{R(2R + X)}{3R + X}$$X(3R + X) = 2R^{2} + RX$$3RX + X^{2} = 2R^{2} + RX$$X^{2} + 2RX - 2R^{2} = 0$Using the quadratic formula $X = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$:$X = \frac{-2R \pm \sqrt{(2R)^{2} - 4(1)(-2R^{2})}}{2(1)}$$X = \frac{-2R \pm \sqrt{4R^{2} + 8R^{2}}}{2}$$X = \frac{-2R \pm \sqrt{12R^{2}}}{2} = \frac{-2R \pm 2R\sqrt{3}}{2}$$X = -R \pm R\sqrt{3}$Since resistance must be positive, we take the positive root:$X = (\sqrt{3} - 1)R$

Two known resistances of $R \ \Omega$ and $2R \ \Omega$ and one unknown resistance $X \ \Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points $A$ and $B$ in the circuit is $X \ \Omega$, then the value of $X$ is . . . . . . $\Omega$.

Similar Questions

$A$ conductor of resistance $3 \Omega$ is stretched uniformly until its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is

The brightness of a bulb will be reduced,if a resistance is connected in

You are given $10$ resistors each of resistance $1 \ \Omega$. First,they are connected to obtain the possible minimum resistance. Then,they are connected to obtain the possible maximum resistance. The ratio of minimum and maximum resistance is . . . . . . .

Two conductors of same length are connected in parallel as shown in the figure. Their cross-sectional areas are $A_1$ and $A_2$ and their resistivities are $\rho_1$ and $\rho_2$ respectively. The equivalent resistivity of this combination is

Vedclass Test Series

Exam Paper Generator

Online Exam Module