PhysicsKund Physics class 9 to 12 NCERT, JEE - NEET

Define Mobility it's S.I unit and Dimensions and Its Relation with Electric Current :  Conductivity in materials arises due to the motion of charge carriers. In metals, the charge carriers are electrons, while in electrolytes and ionised gases both positive and negative ions may contribute. Mobility :  Mobility ($\mu$) is defined as the drift velocity acquired per unit electric field. $\mu = \frac{[v_d]}{E}$ Where: $\mu$= mobility $v_d$= drift velocity E = electric field SI Unit :   $\mu = \frac{m/s}{V/m}$ $\mu =\text{m}^2 \text{V}^{-1}\text{s}^{-1}$ Mobility is always positive. From drift velocity relation, $v_d = \frac{e\tau E}{m}$ Therefore, $\mu = \frac{ \frac{e\tau E}{m}}{E}$ $\mu = \frac{e\tau}{m}$ Where:  e= charge of electron $\tau$ = relaxation time m = mass of electron Relation Between Mobility and Electric Current :  Electric current in a conductor is: $I = n e A v_d$ Since, $v_d = \mu E$ Therefore, $I = n e A \mu E$ Thus, electric current is directly...

limitations of Ohm's law | Distinguish Ohmic and non ohmic circuit elements  Ohm's law is not considered to be a fundamental law. It explains the common behaviour of many substances/materials under given conditions like constant temperature and pressure. It is, therefore, possible that some materials may not strictly follow the Ohm's law (i.e. $V \propto I$). Ohm's law is not obeyed in the following cases : 1. When temperature of a conductor increases considerably . Ohm's law ($V \propto I$ or $R = \frac{V}{I}$) for a conductor at constant temperature is shown by a dotted line in Figure 13. However, when temperature of the conductor increase, its resistance increases and hence $V$ is not directly proportional to $I$. The behaviour of a conductor at high temperature is shown by a solid curve  2. Ohm's law is not obeyed by semiconductor diode. A semiconductor diode conducts, when forward biased and does not conduct, when reverse biased. (We shall discuss semicondu...

Drift of Electrons and the Origin of Resistivity :  Drift Velocity :  Consider a conductor with free electrons moving randomly. When an electric field $\vec{E}$ is applied across the conductor, the electrons experience a force $\vec{F} = -e\vec{E}$, where $-e$ is the charge of an electron. This force causes the electrons to accelerate. According to Newton's second law, $\vec{F} = m\vec{a}$, where $m$ is the mass of the electron and $\vec{a}$ is its acceleration. Therefore, $m\vec{a} = -e\vec{E}$ $\vec{a} = -\frac{e\vec{E}}{m}$ The electrons collide with the ions in the conductor. Let $\tau$ be the average time between successive collisions, known as the relaxation time. The average velocity acquired by the electrons due to the electric field is called the drift velocity $\vec{v}_d$. $\vec{v}_d = \vec{a}\tau = -\frac{e\vec{E}\tau}{m}$ The negative sign indicates that the drift velocity is opposite to the direction of the electric field. Origin of Resistivity :  Let $n$ be ...

Define Resistivity and conductivity | S.I Unit and Dimensions | Factors on depends Resistivity :  $\rho = R \left( \frac{A}{l} \right)$ If $A = 1$, $l = 1$, then $\rho = R$ resistivity of a conductor of a given material is defined as the resistance of the conductor of unit length and unit area of cross-section. S.I. Unit of Resistivity :  Since, $\rho = R \left( \frac{A}{l} \right)$, therefore, S.I. unit of $\rho$ is $\frac{\text{ohm metre}^2}{\text{metre}}$ or ohm-metre ($\Omega$ m) Dimensional formula of resistivity :  Resistivity, $[\rho] = \frac{[R] \times [A]}{[L]} = \frac{[ML^2T^{-3}A^{-2}] [L^2]}{[L]} = [ML^3T^{-3}A^{-2}]$ conductivity :  Electrical conductivity or conductivity of a substance is equal to the inverse of its resistivity. That is, $ \sigma = \frac{1}{\rho}$ S.I. unit of conductivity :  $\Omega^{-1} m^{-1}$ or $Sm^{-1}$. Dimensions of Conductivity :  $[\sigma] = \frac{1}{[\rho]} = [M^{-1}L^{-3}T^3A^2]$ $ \rho = \frac{m}{ne^2\tau$ $ and $...

Factor Affecting the Resistance: Electrical Resistivity or Specific Resistance State the factors on which the resistance of a conductor depends at constant temperature and hence define electrical resistivity or specific resistance. Give SI unit and dimensional formula of specific resistance. Resistance of a conductor at constant temperature depends upon: (a) Length of the conductor: The resistance R of a conductor is directly proportional to its length $l$. That is, $R \propto l \quad \ldots (i)$ More the length of a conductor, more is its resistance. (b) Area of cross-section of the conductor: The resistance of a conductor is inversely proportional to its area of cross-section A. That is, $R \propto \frac{1}{A} \quad \ldots (ii)$ Thus, thin wire has more resistance than the thick wire of same length. Combining eqns. (i) and (ii), we get $R \propto \frac{l}{A}$ or $R = \rho \left( \frac{l}{A} \right) \quad \ldots (iii)$ where, $\rho$ is known as specific resistance or resistivity of th...

Define Resistance and Conductance | SI Unit , Dimensions  Electric Resistance :  Resistance of a conductor is the opposition offered by the conductor to the flow of electric charge in the conductor. Resistance of a conductor is defined as the ratio of the potential difference across the ends of the conductor to the current flowing through it. That is, $R = \frac{V}{I}$ S.I. unit of resistance :  It's S.I unit is ohm ($\Omega$) $1 \text{ ohm } (\Omega) = \frac{1 \text{ volt } (V)}{1 \text{ ampere } (A)} \quad \text{ or } 1 \Omega = 1 VA^{-1}$ Definition of 1 ohm:  Resistance of a conductor is said to be 1 ohm, if current of 1 A flows through it, when potential difference of 1 V is applied across it. Dimensional formula of resistance: $[R] = \frac{[V]}{[I]}$ $[R]= \frac{[\text{Work}]}{[\text{Charge}] \times [\text{Current}]}$ $[R]=\frac{[\text{Work}]}{[\text{Current}] \times [\text{Time}] \times [\text{Current}]}$ $[R]= \frac{[ML^2T^{-2}]}{[A^2T]}$ $[R]= [ML^{2}T^{-3}A...

State and Verify Ohm's Law | Draw V-I Characteristics Statement of Ohm's Law :  According to Ohm's law, the current ($I$) flowing through a conductor is directly proportional to the potential difference ($V$) across the ends of the conductor, provided the physical conditions (like temperature, pressure, strain, etc.) of the conductor remain unchanged. Mathematically, this can be expressed as: $V \propto I$ Introducing a constant of proportionality, $R$, known as the electric resistance or simply resistance of the conductor, we get: $V = RI$ This can also be written as: $R = \frac{V}{I}$ The value of $R$ depends on the nature of the material of the conductor, its dimensions, and temperature. It does not depend on the values of $V$ and $I$. Verification of Ohm's Law :  Ohm's law can be verified using the voltmeter-ammeter method. A circuit is set up with a battery connected to a conductor XY through a rheostat, an ammeter in series, and a key. A voltmeter is connected...

RESISTIVITY OF VARIOUS MATERIALS For ideal conductor, resistivity is zero and for ideal insulator , the resistivity is infinite.  Metals have low resistivities in the range of $10^{-8} \Omega m$ to $10^{-6} \Omega m$. At the other end are insulators like ceramic, rubber and plastics having resistivities $10^{18}$ times greater than metals or more. In between the two are the semiconductors. These, however, have resistivities characteristically decreasing with a rise in temperature. The resistivities of semiconductors can be decreased by adding small amount of suitable impurities.  Resistivity of material is inversely proportional to its conductivity therefore conductivity of conductor is more than that of semiconductor. the conductivity of a semiconductor is more that of an insulator

Discuss the temperature dependence of resistivity of metals/conductors, insulators and semiconductors. It has been observed that at low temperature, resistivity of a conductor increases at a higher power of temperature (T). Thus, over a limited range of temperature, the variation of $\rho$ with temperature (T) is expressed by the relation $\rho = \rho_0 [1 + \alpha (T - T_0)]$ where $\rho_0$ is the resistivity at reference temperature $T_0$ (say 273 K or $0^\circ$C), $\rho$ is resistivity at temperature $T$ and $\alpha$ is the temperature coefficient of resistivity. The temperature coefficient of resistivity is defined as : $\alpha = \frac{(\rho - \rho_0)}{\rho_0 (T - T_0)} = \frac{\Delta \rho}{\rho_0 \Delta T}$ Thus, temperature coefficient of resistivity ($\alpha$) is defined as the change in resistivity per unit original resistivity per unit change in temperature. The SI unit of temperature coefficient of resistivity is (kelvin)$^{-1}$ or K$^{-1}$. Temperature coefficient of resisti...

Define electric energy and power. Give their S.I. units and define them. Give relation between them. Electric Energy : The work done by a source to maintain a current in an electrical circuit is known as electric energy. Consider an electric device or circuit element (e.g., an electric lamp, heater etc.) of resistance $R$ through which current $I$ flows from the end $A$ to the end $B$ for time $t$. Let $q$ be the charge flowing from $A$ to $B$ in time $t$, then $q = It \quad \left( I = \frac{q}{t} \right)$ If $V$ be the potential difference between $A$ and $B$, then work done to carry the charge $q$ from point $B$ to $A$ is equal to the change in potential energy of the charge $q$ and is given by  $W = \Delta U = Vq = VIt$ This work done is equal to the electric energy $E$ consumed in the circuit and is given by E = VIt We know, $V = IR$ (from Ohm's law) $E = (IR) It = I^2Rt = \left( \frac{V}{R} \right)^2 Rt = \frac{V^2}{R} t$ This electric energy appears as heat energy in the res...

Define cell, e.m.f., terminal potential difference and internal resistance of a cell. 1. Define Cell :  A cell is a device which provides the necessary potential difference to an electric circuit to maintain a continuous flow of current in it. A cell consists of two rods or plates called electrodes which are dipped in a chemical solution called electrolyte. The pictorial symbol of a cell is $\dashv \vdash$. Longer vertical line shows +ve terminal and shorter vertical line shows -ve terminal of the cell. 2. EMF (Electromotive force) :  E.M.F. of a cell may be defined as the potential difference between the terminals of the cell when no current is drawn from the cell. In a cell, the positive charges are driven towards an electrode making it positive and the negative charges towards the other electrode making it negative. Thus, a potential difference develops between +ve and -ve electrodes i.e. terminals of the cell. E.M.F. of a cell can also be defined as: The work per unit char...

CELLS IN SERIES AND PARALLEL :  Derive expressions for equivalent e.m.f. and internal resistance of cells connected in series, parallel and mixed combination. Cells can be connected in : (i) series, (ii) parallel, (iii) mixed combination. Cells Connected in Series :  In series combination of the cells, the negative terminal of a cell is connected to the positive terminal of an other cell, and so on. (a) Identical Cells Connected in Series:  Consider $n$ identical cells such as $C_1$, $C_2$, $\dots$, $C_n$ each of e.m.f. $\varepsilon$ and internal resistance $r$ connected in series to an external resistance $R$. Since cells are connected in series, so the total e.m.f. of $n$ cells = $n\varepsilon$. That is,     $\varepsilon_{\text{eff}}= \varepsilon + \varepsilon + \varepsilon + \dots n = n\varepsilon$     $r_{\text{eff}} = r + r + r + \dots \text{upto } n \text{ terms} = nr$ Total resistance = $r_{\text{eff}} + R$ Total resistance = $nr + R$ Hence, eqn...

KIRCHHOFF'S LAWS AND SIMPLE APPLICATIONS :  Question : State and explain Kirchhoff's rules with the help of simple applications. Kirchhoff's laws are used to find the currents and voltages in different parts of the circuit. 1. Kirchhoff's First Law or Rule (The Junction Law or Kirchhoff's Current Law) :  It states that the sum of all the currents entering any point (or junction) must be equal to the sum of all currents leaving that point (junction). The algebraic sum of all the currents meeting at a point (or junction) in a closed electrical circuit is zero. That is, $ \Sigma I = 0 $ Consider a point or junction O in an electrical circuit . Let $I_1$, $I_3$ be the currents entering the point O and $I_2$, $I_4$, $I_5$ be the currents leaving the point O. Then according to Kirchhoff's first law or junction law, $I_1 + I_3 = I_2 + I_4 + I_5 \quad \dots(i)$ or $ I_1 + I_3 + (-I_2) + (-I_4) + (-I_5) = 0 $ or $ I_1 + I_3 - I_2 - I_4 - I_5 = 0$ or  $\Sigma I = 0 \dots(...

Ques : What is Wheatstone bridge? Give its principle, theory and proof. Solution : Wheatstone bridge is an arrangement of four resistors in the form of a bridge used for measuring one unknown resistance in terms of other three known resistances. Construction : Four resistors of resistances $P, Q, R$ and $S$ respectively are arranged in the form of a bridge. A source of e.m.f. '$\epsilon$' is connected between points $A$ and $C$. A galvanometer is connected between points $B$ and $D$. Unknown resistance can be in any of the four arms of the bridge $P, Q, R$ and $S$. Usually, unknown resistance is Put at S. Out of the four resistances, one(S) is unknown, one is variable (R) and the other two (P and Q) can be standard resistors. Principle : When key K is closed, the galvanometer shows the presence of current $I_g$ through it. The value of a resistances say R is adjusted in such a way that the galvanometer shows no deflection. At this stage, the potential at points B and D is equa...

NCERT Solutions Class 12 Physics Chapter 3 Current Electricity with Video Explanation Question 3.1 : The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4Ω, what is the maximum current that can be drawn from the battery? Solution :   $$ I_{max} = \frac{E}{r}=\frac{12}{0.4}$$ $$I_{max} = 30 A$$ Question 3.2 : A battery of e.m.f 10V and internal resistance 3Ω is connected to a resistor. If The current in the circuit is 0.5A, what is the resistance of the resistor ? What is the terminal voltage of the battery when the circuit is closed ?  Solution :   $$ I = \frac{E}{R+r}$$ $$R+r = \frac{E}{I}$$ $$R+r=  \frac{10}{.5}=20$$ $$Or\;R = 20 - r = 20 - 3$$ $$R = 17 Ω$$ $$Terminal \ Voltage = IR$$ $$V= IR$$ $$V=0.5×17=8.5Volt$$ Question 3.3 : At room temperature (27.0 °C) the resistance of a heating element is 100 Ω. What is the temperature of the element if the resistance is found to be 117 Ω, given that the temperature coefficient...

Notes for Class 12 Physics Chapter 3 Current Electricity is prepared and uploaded for reference by academic team of expert members. 1. Electric current. 2. Flow of electric charges in a metallic conductor. 3. Drift velocity . 4. Mobility and their relation with electric current. 5. Ohm's law, V-I characteristics (linear and non-linear). 6. Limitations of Ohm's law | Distinguish Ohmic and non-ohmic circuit elements. 7. Electrical energy and power. 8. Electrical resistivity and conductivity . 9. Temperature dependence of resistance . 10. Internal resistance of a cell, potential difference and emf of a cell. 11. Combination of Cells in Series, Parallel and Group. 12. Kirchhoff's rules. 13. Wheatstone bridge.

Derive relation between e.m.f. and terminal potential difference and thus find expression for internal resistance. Consider a cell of e.m.f. $\varepsilon$ and internal resistance $r$ connected to an external resistance $R$ through a key (K). Case 1 : When key (K) is closed , current is drawn from the cell by the circuit, which is given by $$I = \frac{\varepsilon}{R+r}$$ R and r are in series, so (R + r) is the equivalent resistance of the circuit. $\varepsilon = IR + Ir$ ...(i) According to Ohm's law :  That is, $V = IR$ ...(ii) Hence equation (i) becomes $\varepsilon = V + Ir$ $V = \varepsilon - Ir$...(iii) This shows that the terminal potential difference of the cell is less than the e.m.f. of the cell. Now the voltmeter connected across the cell will read the value as $V$ which is less than the value of e.m.f. ($\varepsilon$). Case 2 : When key (K) is open, $I = 0$ Hence eqn. (iii) becomes $V = \varepsilon$ Thus, terminal potential difference between the electrodes of the cell ...

In a metal Conductor, there are extremely large number of free electrons. These free electrons move randomly with a thermal speed of the order of $10^{5}$ to $10^{6}$ m/s at room temperature.Im any portion of the conductor, the flow of electrons is so oriented that the average thermal velocity of total number of free electrons in a conductor is zero.  That is  $U_{av}= \frac{u_1+u_2+u_3+u_4+u_5....u_6}{n}$ $U_{av} = 0$ Where $u_1 , u_2 , u_3 , u_4 ...... u_n$ are thermal velocities of free electrons and n is the total number of free electrons. When an electric field is applied across the conductor , the free electrons accelerate in a direction opposite to the direction of the applied field. Due to this acceleration, the electrons gain extra velocity but for a short time because the accelerated electrons collide with the ions in the conductor and during this collision , the extra velocity gained is destroyed . Again , the electron is Accelerated and comes to rest after collisio...

Define electric current. What is the direction of electric current? State and define S.I. unit of electric current. What is the nature of electric current? Give types of current. ELECTRIC CURRENT :  Electric current: Electric current is defined as the amount of electric charges flowing through any cross-section of a conductor per unit time. Let charge $Q$ crosses through a cross-section of a conductor in time $t$, then $I = \frac{\text{Total charge flowing (Q)}}{\text{Time taken (t)}}$ $I = \frac{Q}{t} \quad \dots (1)$ If $n$ electrons, each of charge $e$ ($= 1.6 \times 10^{-19}$), cross through a cross-section of a conductor in time $t$, then total charge passing through a cross-section of the conductor is given by, $Q = ne$. Hence, $ I = \frac{Q}{t} = \frac{ne}{t} \quad \dots(2) $ Electric current defined by eqn. (1) is known as steady current. If the net charge $\Delta Q$ crosses the shaded cross-sectional area of the conductor in a time $\Delta t$, then the average electric cur...

Current carriers :  The charged particles which constitute an electric current in solids , liquids or gases are knowns as current carriers. a) Solids :  In conductors (e.g. metal like Copper , Silver , Aluminium Etc ) , Free Electrons constitute an electric current.  Electrons in the outermost orbits of the atoms ( Valence electrons) of conductors are loosely bound. These electrons can move about in the whole conductor are known as Free Electrons. Under the effect of external electric field , these free electron move in a direction opposite to the direction of the external field and constitute electric current.  Free electrons or valance electrons are the current carriers in conductors.  In insulators  , all the electrons are tightly bound to their parent atoms . Hence they do not have free electrons and as such there is practically no current carrier in an insulator. In semi conductor, the current carriers are free electrons and holes. b) Liquids :  S...