In the figure shown,for given values of R_1 a | vedclass

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

Question

(A) Let the resistance per unit length of the wire be $\sigma$. The total length $AB = 100\, cm$.Case $1$: Balance point is at $40\, cm$ from $A$.Usin

Vedclass · Accepted Answer

$\frac{10}{3}\,\Omega, 5\,\Omega$

Vedclass · Answer

(A) Let the resistance per unit length of the wire be $\sigma$. The total length $AB = 100\, cm$.Case $1$: Balance point is at $40\, cm$ from $A$.Using the Wheatstone bridge principle: $\frac{R_1}{R_2} = \frac{\sigma 	imes 40}{\sigma 	imes (100 - 40)} = \frac{40}{60} = \frac{2}{3}$.So,$R_1 = \frac{2}{3} R_2$  --- $(1)$Case $2$: $R_2$ is shunted by $10\,\Omega$. The new resistance $R_2' = \frac{R_2 	imes 10}{R_2 + 10}$.The balance point shifts to $50\, cm$.Using the principle: $\frac{R_1}{R_2'} = \frac{50}{50} = 1$.So,$R_1 = R_2' = \frac{10 R_2}{R_2 + 10}$ --- $(2)$Equating $(1)$ and $(2)$:$\frac{2}{3} R_2 = \frac{10 R_2}{R_2 + 10}$$2(R_2 + 10) = 30$$2 R_2 + 20 = 30$$2 R_2 = 10 \implies R_2 = 5\,\Omega$.Substituting $R_2 = 5\,\Omega$ in $(1)$:$R_1 = \frac{2}{3} 	imes 5 = \frac{10}{3}\,\Omega$.

In the figure shown,for given values of $R_1$ and $R_2$,the balance point for the jockey is at $40\, cm$ from $A$. When $R_2$ is shunted by a resistance of $10\,\Omega$,the balance point shifts to $50\, cm$. Find $R_1$ and $R_2$ $(AB = 1\, m)$.

Similar Questions

In which interval is the function $f(x) = 2x^2 - \ln |x|, (x \neq 0)$ monotonically decreasing?

The set of values of $x$ for which the inequalities $x^2-3x-10 < 0$ and $10x-x^2-16 > 0$ hold simultaneously,is

$A$ block of mass $0.50 \ kg$ is moving with a speed of $2.00 \ ms^{-1}$ on a smooth surface. It strikes another mass of $1.00 \ kg$ (initially at rest) and then they move together as a single body. The energy loss during the collision is .............. $J$

Which of the following is the strongest Bronsted base?

On adding $AgNO_3$ solution into $KI$ solution,a negatively charged colloidal sol is obtained when they are in:

Vedclass Test Series

Exam Paper Generator

Online Exam Module