Physics Vidyapith ✍️

There are the following differences between a potentiometer and a voltmeter given below: Potentiometer: 1.) It is based on null method. 2.) It gives an accurate value of emf. 3.) While measuring emf, it does not draw any current from the cell. 4.) Resistance of potentiometer wire becomes infinite while measuring emf. 5.) It can be used for various experimental purposes. 6.) It can not be taken conveniently from one place to another place. Voltmeter: 1.) It is based on the deflection method. 2.) It does not give an accurate value of emf. 3.) While measuring emf, it draws some current from the cell. Hence it reads slightly less than the actual emf. 4.) The resistance of the voltmeter is high enough but not infinite. 5.) It can be used to measure potential differences only. 6.) It can be conveniently taken from one place to another place.

Potentiometer- An ideal voltmeter that does not change the original potential difference, needs to have infinite resistance. But a voltmeter cannot be designed to have infinite resistance. The potentiometer is one such instrument that does not draw any current from the circuit and still measures the potential difference. so it behaves as an ideal voltmeter. "A potentiometer is an instrument. This is used to measure the potential difference between two points of an electric circuit and emf of a cell." Principle- The principle of the potentiometer depends upon the potential gradient along the wire i.e. "When a constant current flows in a wire then the potential drops per unit length of the wire". Construction- A potentiometer consists of a long wire $AB$ of uniform cross-section, usually, this wire is $4 m$ to $10 m$ long and it is made of the material having high resistivity and low-temperature coefficient such as manganin or constant. Usually,

What is Metre Bridge? It is the simplest practical application of the Wheatstone's bridge that is used to measure an unknown resistance. Principle: Its working is based on the principle of Wheatstone's Bridge. When the Wheatstone's bridge is balanced $\frac{P}{Q}=\frac{R}{S}$ Construction: It consists of usually one-meter long manganin wire of uniform cross-section, stretched along a meter scale fixed over a wooden board and with its two ends soldered to two L-shaped thick copper strips $A$ and $C$. Between these two copper strips, another copper strip is fixed so as to provide two gaps $mn$ and $m_{1}n_{1}$. A resistance box (R.B.) is connected in the gap $mn$ and the unknown resistance $S$ is connected in the gap $m_{1}n_{1}$. A cell of emf $E$, Key $(K)$, and rheostat are connected across $AC$. A movable jockey and a galvanometer are connected across the $BD$, as shown in the figure. Metre Bridge Or Slide Wire Bridge Working: In

It is an arrangement of four resistance used to determine one of this resistance quickly and accurately in terms of the remaining three resistance. Objective: To find the unknown resistance with the help of the remaining three resistance. Principle of Wheatstone Bridge:  The principle of Wheatstone bridge is based on the principle of Kirchhoff's Law. Construction: A Wheatstone bridge consists of four resistance $P$,$Q$,$R$, and $S$. This resistance is connected to form quadrilateral $ABCD$. A battery of EMF $E$ is connected between point $A$ and $C$ and a sensitive galvanometer is connected between point $B$ and $D$ Which is shown in the figure below. Diagram of Wheatstone's Bridge Working: To find the unknown resistance $S$, The resistance $R$ is to be adjusted like there is no deflection in the galvanometer. which means that there is not any flow of current in the arm $BD$. This condition is called "Balanced Wheatstone bridge" i.e

Kirchhoff's laws:  Kirchhoff had given two laws for electric circuits i.e. Kirchhoff's Current Law or Junction Law Kirchhoff's Voltage Law or Loop Law Kirchhoff's Current Law or Junction Law: Kirchhoff's current law state that The algebraic sum of all the currents at the junction in any electric circuit is always zero. $\sum_{1}^{n}{i_{n}}=0$ Sign Connection:   While applying the KCL, the current moving toward the junction is taken as positive while the current moving away from the junction is taken as negative. The flow of Current in a junction So from figure,the current $i_{1}$,$i_{2}$,$i_{5}$ is going toward the junction and the current $i_{3}$,$i_{4}$, So $\sum{i}= i_{1}+i_{2}+(-i_{3})+(-i_{4})+i_{5}$ According to KCL $\sum{i}= 0$, Now the above equation can be written as $i_{1}+i_{2}+

Theory of Free Electron Gas Model → According to the electron gas theory 1. The free electrons are continuous in motion inside the metal. The motion of free electrons are random inside the metal. 2. When the free electrons are collisied to each other then the direction of electrons are changed. 3. Mean free Path: The length covered by free electrons, between the two successive collisions is called the "Mean Free Path". 4.  Relaxation Time: The time taken between the two successive collisions of free electrons is called the Relaxation time. It is represented by $\tau$. 5. Drift velocity: When a potential is applied across the metal then these electrons do not move own velocity but it move with an average velocity in the opposite direction of the electric field. This average velocity is called the "Drift Velocity". The drift velocity of electrons depends upon the applied potential. 6. Mobility of Electrons: When a potential $V$ is

Derivation→ Let us consider, The length of the conductor = $l$ The cross-section area of the conductor = $A$ The potential difference across the conductor = $V$ The drift velocity of an electron in conductor = $v_{d}$ Now from the equation of the mobility of electron i.e. $v_{d}= \mu E$ $v_{d}= \left( \frac{e\tau}{m} \right) E \qquad \left(\because \tau = \frac{e\tau}{m} \right)$ $v_{d}= \left( \frac{e\tau}{m} \right) \frac{V}{l}\qquad (1) \qquad \left(\because E = \frac{V}{l} \right)$ Now from the equation of drift velocity and electric current $i=neAv_{d}$ Now substitute the value of $v_{d}$ from equation $(1)$ to above equation $i=neA\left( \frac{e\tau}{m} \right) \frac{V}{l}$ $i=\left( \frac{ne^{2}A\tau}{ml} \right)V$ $\frac{V}{i}=\left( \frac{ml}{ne^{2}A\tau} \right)$ $\frac{V}{i}=R$ Where $R = \frac{ml}{ne^{2}A\tau} $ is known as electrical resistance of the conductor. Thus $V=iR$ This is Ohm's Law.

Derivation→ Let us consider The length of the conductor = $l$ The cross-section area of the conductor = $A$ The total number of free electrons inside the conductor = $N$ The current flow in the conductor = $i$ The flow of Electron in Conductor The Relaxation time between the two successive collisions =$\tau$ According to the law of current density $J=\frac{i} {A} $ $J=\frac{q} {A \tau} \qquad \left( \because i=\frac{q}{\tau} \right)$ $J=\frac{N \: e }{A \tau} \qquad \left( \because q=Ne \right)$ Now multiply by length of conductor $l$ in above equation. Therefore we get $J=\frac{N \: e \: l}{A \tau\: l} $ $J=\frac{N \: e \: l}{V \tau\: }\qquad \left(\because V=A.l \right)$ Where $V$ is volume of the conductor. $J=\frac{n \: e \: l}{ \tau }\qquad \left( \because n=\frac{N}{V} \right)$ Where $n$ is total number of electrons per unit . $J=n \: e \: v_{d}\qquad \left( \because v_{d}=\frac{l}{\tau}\right)$ Whe