Physics · Class 12 Science
Ch 3Current Electricity — concept-first.
In earlier chapters, we studied charges at rest — electrostatics. But in real life, charges often move. This motion of charges is called an electric current. Some currents, like lightning, are sudden and unsteady.
Key concepts
Hover a concept to preview it and jump to its most relevant questions.
Drift Velocity
Electrons in a metal are always moving — but randomly. At room temperature they zip around at roughly m/s, colliding with the lattice ions every few trillionths of a second.
Most relevant questions
- (a) Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area $1.0 \times 10^{-7}\ \text{m}^2$ carry…Free
- (a) In Example 3.1, the electron drift speed is estimated to be only a few $\text{mm s}^{-1}$ for currents in the range of a few amperes? Ho…Preview
- The number density of free electrons in a copper conductor estimated in Example 3.1 is $8.5 \times 10^{28}\ \text{m}^{-3}$. How long does an…Preview
- Consider a current carrying wire (current $I$) in the shape of a circle. Note that as the current progresses along the wire, the direction o…Free
- Which of the following characteristics of electrons determines the current in a conductor? (a) Drift velocity alone. (b) Thermal velocity al…Preview
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
In earlier chapters, we studied charges at rest — electrostatics. But in real life, charges often move. This motion of charges is called an electric current.
Electric Current
Electric current is fundamentally about the net flow of charge across a given area. It is not simply the total charge moving, but the net amount—the difference between charge flowing forward and backw…
Electric Currents in Conductors
In a conductor, some electrons are free — not bound to any particular nucleus. When no electric field is present, these electrons move randomly due to thermal energy.
Ohm's Law
Ohm’s law is a basic experimental law discovered by G.S. Ohm in 1828. It describes the relationship between the current flowing through a conductor and the potential difference across its ends.
Drift of Electrons and the Origin of Resistivity
In a metal, free electrons are in constant, random motion, colliding with the fixed positive ions. Without an electric field, these collisions randomise velocities so thoroughly that the average veloc…
+−Worked Examplesi2 questions
- Example 3.1(a) Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area $1.0 \times 10^{-7}\ \text{m}^2$ carry…Free
- Example 3.2(a) In Example 3.1, the electron drift speed is estimated to be only a few $\text{mm s}^{-1}$ for currents in the range of a few amperes? Ho…Preview
Mobility
Mobility quantifies how quickly a charge carrier (like an electron or ion) can drift through a material when an electric field is applied. It is a measure of the "ease" with which the carrier moves.
Limitations of Ohm's Law
Ohm’s law states that for many conductors, the current is directly proportional to the applied voltage :
Resistivity of Various Materials
Materials are grouped into conductors, semiconductors, and insulators based on their resistivity values, arranged from lowest to highest.
Temperature Dependence of Resistivity
Resistivity () is not a fixed property of a material — it changes with temperature. The way it changes depends on the type of material: metals, alloys, and semiconductors behave differently.
+−Worked Examplesi2 questions
- Example 3.3An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it, its resistance at room tempera…Free
- Example 3.4The resistance of the platinum wire of a platinum resistance thermometer at the ice point is $5\ \Omega$ and at steam point is $5.23\ \Omega…Preview
Electrical Energy, Power
When current flows through a conductor, the moving charges (electrons) collide with the atoms of the material.
Cells, EMF, Internal Resistance
A cell is a device that maintains a steady current in a circuit by converting chemical energy into electrical energy.
Cells in Series and in Parallel
Just as resistors can be connected in series or parallel to get a desired equivalent resistance, cells (batteries) can also be combined.
Kirchhoff's Rules
Simple series and parallel resistor formulas are not enough for many circuits. When resistors and cells are interconnected in a complicated way, we need two general rules — Kirchhoff’s junction rule a…
+−Worked Examplesi2 questions
- Example 3.5A battery of $10\ \text{V}$ and negligible internal resistance is connected across the diagonally opposite corners of a cubical network cons…Free
- Example 3.6Determine the current in each branch of the network shown in Fig. 3.17.  the resistance of a heating element is $100\ \Omega$. What is the temperature of the element if…Free
- 3.4A negligibly small current is passed through a wire of length $15\ \text{m}$ and uniform cross-section $6.0 \times 10^{-7}\ \text{m}^2$, and…Preview
- 3.5A silver wire has a resistance of $2.1\ \Omega$ at $27.5\ ^\circ\text{C}$, and a resistance of $2.7\ \Omega$ at $100\ ^\circ\text{C}$. Deter…Preview
- 3.6A heating element using nichrome connected to a $230\ \text{V}$ supply draws an initial current of $3.2\ \text{A}$ which settles after a few…Preview
- 3.7Determine the current in each branch of the network shown in Fig. 3.20.  in the shape of a circle. Note that as the current progresses along the wire, the direction o…Free
- Q2Two batteries of emf $\varepsilon_1$ and $\varepsilon_2$ (with $\varepsilon_2 > \varepsilon_1$) and internal resistances $r_1$ and $r_2$ res…Free
- Q5A metal rod of length $10\ \text{cm}$ and a rectangular cross-section of $1\ \text{cm} \times \tfrac{1}{2}\ \text{cm}$ is connected to a bat…Free
- Q6Which of the following characteristics of electrons determines the current in a conductor? (a) Drift velocity alone. (b) Thermal velocity al…Preview
- Q7Kirchhoff's junction rule is a reflection of (a) conservation of current density vector. (b) conservation of charge. (c) the fact that the m…Preview
- Q8In a simple circuit, a cell of emf $V$ and internal resistance $r$ drives current through two resistors that are connected in parallel betwe…Preview
- Q9Temperature dependence of resistivity $\rho(T)$ of semiconductors, insulators and metals is significantly based on the following factors: (a…Preview
- Q10An unknown resistance $R$ is measured with a Wheatstone bridge having two ratio-arm resistances $R_1$ and $R_2$ and a known standard resista…Preview
- Q12Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why not?Preview
- Q13The relaxation time $\tau$ is nearly independent of applied $E$ field whereas it changes significantly with temperature $T$. First fact is (…Preview
- Q14What are the advantages of the null-point method in a Wheatstone bridge? What additional measurements would be required to calculate $R_{unk…Preview
- Q16For wiring in the home, one uses Cu wires or Al wires. What considerations are involved in this?Preview
- Q17Why are alloys used for making standard resistance coils?Preview
- Q18Power $P$ is to be delivered to a device via transmission cables having resistance $R_C$. If $V$ is the voltage across $R$ and $I$ the curre…Preview
- Q21A cell of emf $E$ and internal resistance $r$ is connected across an external resistance $R$. Plot a graph showing the variation of P.D. acr…Preview
- Q22First a set of $n$ equal resistors of $R$ each are connected in series to a battery of emf $E$ and internal resistance $R$. A current $I$ is…Preview
- Q23Let there be $n$ resistors $R_1 \ldots R_n$ with $R_{max} = \max(R_1 \ldots R_n)$ and $R_{min} = \min\{R_1 \ldots R_n\}$. Show that when the…Preview
- Q24Two cells are connected in opposition to each other, forming a single closed loop with no external resistor. Cell $E_1$ has emf $6\ \text{V}…Preview
- Q25Two cells of the same emf $E$ but different internal resistances $r_1$ and $r_2$ are connected in series with each other and with an externa…Preview
- Q26Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter $1\ \text{mm}$. Conductor $…Preview
- Q27Suppose there is a circuit consisting of only resistances and batteries and we have to double (or increase it to $n$-times) all voltages and…Preview
- Q28Two cells are connected in parallel in opposition: one cell has emf $10\ \text{V}$ and internal resistance $10\ \Omega$, the other has emf $…Preview
- Q29A room has AC run for 5 hours a day at a voltage of $220\ \text{V}$. The wiring of the room consists of Cu of $1\ \text{mm}$ radius and a le…Preview
- Q31A resistor $R = 6\ \Omega$ is connected across a battery of emf $V = 6\ \text{V}$ of negligible internal resistance, forming a single loop i…Preview