Question: Q. 4. Following circuit was set up in a meter bridge experiment to determine the value $X$ of an unknown resistance.

(a) Write the formula to be used for finding $X$ from the observations.

(b) If the resistance $R$ is increased, what will happen to balancing length? R&U [CBSE SQP 2018-19]

Sol. (a) $X=(100-l) R / l$

(b) Balancing length will increase in increase of resistance $R$.

[CBSE Marking Scheme 2018]

Q. 5. In a potentiometer arrangement for determining the emf of a cell, the balance point of the cell in open circuit is $350 \mathrm{~cm}$. When a resistance of $9 \Omega$ is used in the external circuit of the cell, the balance point shifts to $300 \mathrm{~cm}$. Determine the internal resistance of the cell.

A [ Delhi & O.D. 2018] Sol. Stating the formula 1

Calculating $r$

1

We have, $\quad r=\left(\frac{l_{1}}{l_{2}}-1\right) R=\left(\frac{l_{1}-l_{2}}{l_{2}}\right) R \quad 1$

$\therefore \quad r=\left(\frac{350-300}{300}\right) \times 9 \Omega$

$=\frac{50}{300} \times 9 \Omega=1.5 \Omega$

$1 / 2$

[CBSE Marking Scheme, 2018]

Short Answer Type Questions-II

Q. 1. (i) Write the principle of working of a metre bridge.

(ii) In a metre bridge, the balance point is found at a distance $l_{1}$ with resistances $R$ and $S$ as shown in the figure.

An unknown resistance $X$ is now connected in parallel to the resistance $S$ and the balance point is found at a distance $l_{2}$. Obtain a formula for $X$ in terms of $l_{1}, l_{2}$ and $S$.

A [O.D. I, II, III 2017]

Show Answer

Solution:

Ans. (i) Principle of metre bridge

1

(ii) Relation between $I_{1}, I_{2}$, and $S$

2

(i) The principle of working of a metre bridge is same as that of a balanced Wheatstone bridge.

Alternatively

When $\quad i_{G}=0$, then $\frac{P}{Q}=\frac{R}{S} \quad 1 / 2$

(ii)

$$ \frac{R}{S}=\frac{l_{1}}{100-l_{1}} $$

$1 / 2$

When $X$ is connected in parallel :

$$ \frac{R}{\left(\frac{X S}{X+S}\right)}=\frac{l_{2}}{100-l_{2}} $$

On solving we get, $X=\frac{l_{1} S\left(100-l_{2}\right)}{100\left(l_{2}-l_{1}\right)}$

1

[CBSE Marking Scheme 2017]

OR

Ans. (i)

Princeple of workeng of a metec beidge

The pecncipce is Wheatsen principce

If foce eescisances $D, Q, R$ ands aeconneded

in the whealstone beidge in the foclowing

manner, then at balanced condction, 2 cuerenc

in the galvanomelice is $2 e x 0$ on the

lescseance can be fornd:

(ii)

[II Q. 2. Draw a circuit diagram of a potentiometer. State its working principle. Derive the necessary formula to describe how it is used to compare the emfs of the two cells.

DiO.D. I, II, III 2015]

Ans. The circuit diagram of the potentiometer, is as shown here:

Working Principle :

The potential drop, $V$, across a length $l$ of a uniform wire, is proportional to the length $l$ of the wire. $1 / 2$ or, $\quad \mathrm{V} \propto l \quad$ (for a uniform wire) Derivation : From the figure, connect points 1 and 3 together with balance point at point $N_{1}$ where $A N_{1}=l_{1}$ Now connect points 2 and 3 together with balance point at point $N_{2}$ where $\mathrm{AN}{2}=l{2}$. $1 / 2$ We have,

So,

and

$E_{1}=k l_{1}$ $E_{2}=k l_{2}$

$$ \frac{E_{1}}{E_{2}}=\frac{l_{1}}{l_{2}} $$

$1 / 2$



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