In a meter-bridge experiment,a resistance of | vedclass

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

Question

(C) In a meter-bridge,the balance condition is given by $\frac{P}{Q} = \frac{\ell}{100-\ell}$.For the first case: $\frac{18}{\ell_{1}} = \frac{R}{100-

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(C) In a meter-bridge,the balance condition is given by $\frac{P}{Q} = \frac{\ell}{100-\ell}$.For the first case: $\frac{18}{\ell_{1}} = \frac{R}{100-\ell_{1}}$ ... $(1)$For the second case: $\frac{18}{1.5 \ell_{1}} = \frac{R/3}{100-1.5 \ell_{1}}$ ... $(2)$From equation $(1)$,we have $\frac{R}{18} = \frac{100-\ell_{1}}{\ell_{1}} = \frac{100}{\ell_{1}} - 1$.From equation $(2)$,$\frac{R/3}{18} = \frac{100-1.5 \ell_{1}}{1.5 \ell_{1}} = \frac{100}{1.5 \ell_{1}} - 1$.Dividing equation $(1)$ by equation $(2)$: $\frac{18/\ell_{1}}{18/(1.5 \ell_{1})} = \frac{R/(100-\ell_{1})}{(R/3)/(100-1.5 \ell_{1})}$$1.5 = 3 	imes \frac{100-1.5 \ell_{1}}{100-\ell_{1}}$$0.5 = \frac{100-1.5 \ell_{1}}{100-\ell_{1}}$$50 - 0.5 \ell_{1} = 100 - 1.5 \ell_{1}$$1.0 \ell_{1} = 50 \implies \ell_{1} = 50 	ext{ cm}$.Substituting $\ell_{1} = 50$ in equation $(1)$: $\frac{18}{50} = \frac{R}{100-50} \implies \frac{18}{50} = \frac{R}{50} \implies R = 18 \Omega$.

Similar Questions

Two known resistances are connected in two gaps of a meter bridge. The null point is obtained at $20 \ cm$ from the zero end. $A$ resistance of $15 \ \Omega$ is connected in series with the smaller of the two. The null point shifts to $40 \ cm$. The smaller resistance is (in $\Omega$)

In a meter bridge,the gaps are enclosed by resistances of $2 \ \Omega$ and $3 \ \Omega$. The value of shunt to be added to the $3 \ \Omega$ resistor to shift the balancing point by $22.5 \ cm$ is (in $\Omega$)

In a meter bridge experiment,when a nichrome wire is in the right gap,the balancing length is $60 \ cm$. When the nichrome wire is uniformly stretched to increase its length by $20 \%$,and again connected in the right gap,the new balancing length is nearly: (in $cm$)

In a meter bridge experiment,to minimize an error due to contact resistance,

Vedclass Test Series

Exam Paper Generator

Online Exam Module