Potentiometer and Wheatstone Bridge

In a meter bridge balance point is found at a distance  $l_1$  with resistances R and S as shown in the figure.



When an unknown resistance X is connected in parallel with the resistance S, the balance point shifts to a distance $l_2$ . Find the expression for X in terms of  $l_1$ ,  $l_2$  and S.

A moving coil galvanometer on connecting with a high resistance in series is converted into:

The reading on a high resistance voltmeter, when a cell is connected across it, is 2.5 V. When the terminals of the cell are also connected to resistance of  $5 \mathrm{\Omega }$  as shown in the circuit, the voltmeter reading drops to 2.0 V. The internal resistance of the cell is:

The magnitude of resistance $\mathrm{X}$  in the circuit shown in the given figure, when no current flows through the  $\mathrm{5 }\mathrm{\Omega }$  resistor is

A battery of $6 \mathrm{V}$ is connected to the circuit as shown below. The current $I$ drawn from the battery is

The current $I$ in the given circuit will be

Two tangent galvanometers $A$ and $B$ have coils of radii $8 \mathrm{cm}$ and $16 \mathrm{cm}$ respectively and resistance $8 \mathrm{\Omega }$ each. They are connected in parallel with a cell of emf $4 \mathrm{V}$ and negligible internal resistance. The deflections produced in the tangent galvanometers $A$ and $B$ are $30° \text{and} 60°$ respectively. If $A$ has $2$ turns, then the number of turns $B$ must have is

A galvanometer of resistance $\mathrm{30 }\mathrm{\Omega }$ is connected to a battery of emf $\mathrm{2\; V}$ with $\mathrm{1970 }\mathrm{\Omega }$ resistance in series. A full scale deflection of $20$ divisions is obtained in the galvanometer. To reduce the deflection to $10$ divisions, the resistance in series required is____$\mathrm{\Omega }$.

The deflection in galvanometer falls to ${\left(\frac{1}{4}\right)}^{th}$, when it is shunted by $3 \Omega$ . If additional shunt of $\mathrm{2 \Omega }$ is connected in parallel to earlier shunt, the deflection in galvanometer falls to ${\left(\frac{1}{\alpha }\right)}^{th}$ value. Write the value of $2\alpha$.

Figure shows an unbalanced Wheatstone bridge. What is the direction of conventional current between $B$ and $D$?

The figure given below shows a network of eight resistors, each equal to $2 \mathrm{\Omega },$ connected to a $3 \mathrm{V}$ battery of negligible internal resistance. The current $I$ in the circuit is 

Find the equivalent resistance between $X$ and $Y$.

A cell of $2\mathrm{V},\mathrm{ }1\mathrm{\Omega }$ is balanced at $1.9\mathrm{ }\mathrm{m}$. Then what is balanced length for ideal cell of $2\mathrm{V}$ ?

The current $I$ drawn from the $5 V$ source will be

A galvanometer having a coil resistance of $100\mathrm{ }\mathrm{\Omega }$ gives a full-scale deflection, when a current of $1 \mathrm{mA}$ is passed through it. The value of the resistance, which can convert this galvanometer into an ammeter giving a full scale deflection for a current of $10 \mathrm{A}$, is:

The figure shows a circuit diagram of a Wheatstone bridge to measure the resistance $G$ of the galvanometer. The relation $\frac{P}{Q}=\frac{R}{G}$ will be satisfied only when

On interchanging the resistances, the balance point of a meter bridge shifts to the left by $10 \mathrm{cm}$10 cm. The resistance of their series combination is $\mathrm{1 }\mathrm{k\Omega }$ . How much was the resistance on the left slot before interchanging the resistances?

A $10\mathrm{V}$ battery with internal resistance $\mathrm{1\hspace{0.17em}}\mathrm{\Omega }$ and a $15\mathrm{V}$ battery with internal resistance $\mathrm{0.6 }\mathrm{\Omega }$ are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to:

 In the following figure, the $p.d.$ between the points $M$ and $N$ is balanced against $50 \mathrm{cm}$ length of potentiometer wire of total length $100 \text{cm}$. In order to balance the potential difference between the points $N$ and $C$ the jockey to be pressed on potentiometer wire at a distance of $\left(\text{in cm}\right)$:

The potential gradient of potentiometer is $0.2 \mathrm{volt} {\mathrm{m}}^{-1}$. $A$ current of $0.1 \mathrm{amp}$ is flowing through $a$ coil of $2 \mathrm{Ohm}$ resistance. The balancing length in meters for the$\mathrm{p}.\mathrm{d}.$ at the ends of this coil will be