Chapter 3 · Introduction

Chapter 3 — Current Electricity

Charges on the move: currents, drift velocity and Ohm's law, the resistivity of real materials, cells with internal resistance, and Kirchhoff's rules for any circuit — with the Wheatstone bridge as the finale.

Every evening around 7 pm, India's national power grid meets one of its biggest demand peaks of the day as hundreds of millions of lights, fans and televisions are switched on. Behind each switch is the same simple chain: a source keeps a potential difference, a closed conducting path lets charge flow, and devices turn the energy of the moving charge into light, heat and motion. Yet the details are full of surprises. The electrons in a house wire crawl along at a hundredth of a millimetre per second, while the light comes on instantly; a $60$ W bulb has a resistance of about $880\ \Omega$ when lit and only a few tens of ohms when cold; a car battery's voltage sags while the starter turns.

This chapter explains all of these. We define current and current density and look inside a metal to see how drifting electrons, colliding with the lattice every $10^{-14}$ s or so, produce Ohm's law and the resistivity of copper. We compare materials and their behaviour with temperature, and count the energy and power that circuits deliver. Then we turn to the sources: the emf and internal resistance of a cell, and cells in series and parallel. Finally, Kirchhoff's rules — conservation of charge and of energy written for circuits — let us solve any network, and the Wheatstone bridge shows how a galvanometer reading zero can measure resistance precisely.

Current & current density→Drift velocity→Ohm's law & resistivity→Temperature & power→EMF & internal resistance→Kirchhoff's rules→Wheatstone bridge
🎯 By the end of this chapter you can…
  • define current, current density, drift velocity, relaxation time and mobility, and derive $I=neAv_d$ and $\rho=m/(ne^2\tau)$;
  • use Ohm's law and $R=\rho l/A$, recognise ohmic and non-ohmic devices, and explain how resistivity depends on the material and the temperature;
  • calculate electrical power and energy ($P=VI=I^2R=V^2/R$, kWh), including transmission losses;
  • use emf and internal resistance ($V=\varepsilon\mp Ir$) and find the equivalent of cells in series and in parallel;
  • solve multi-loop circuits with Kirchhoff's junction and loop rules, and derive and use the balance condition of the Wheatstone bridge;
  • solve board, JEE Main, JEE Advanced and NEET problems on all of the above.
Teaser — Why Does the Lamp Light at Once?

Close the switch. The glowing front shows the electric field spreading round the circuit — in reality at about two-thirds of the speed of light, so it is slowed down here more than a billion times. As soon as it arrives, the electrons everywhere — including those in the lamp — start drifting together. The dots show that drift, exaggerated enormously. Compare the two times in the readouts.

current $I$—
drift speed $v_d$ (copper)—
time for an electron to go round—
time for the field to go round—

Sections in this chapter

3.1

Electric Current, Drift Velocity and Ohm's Law

Current and current density, Ohm's law and resistivity, the drift of free electrons, relaxation time and mobility.

$I=neAv_d$, $\ \rho=\dfrac{m}{ne^2\tau}$
Open section →3.2

Resistivity, Its Temperature Dependence and Electrical Power

Non-ohmic devices, resistivities of materials, the temperature coefficient, Joule heating and power transmission.

$\rho_T=\rho_0[1+\alpha(T-T_0)]$, $\ P=I^2R$
Open section →3.3

Cells, EMF, Internal Resistance and Combinations of Cells

What emf means, terminal voltage while discharging and charging, and cells in series and in parallel.

$V=\varepsilon-Ir$, $\ I=\dfrac{\varepsilon}{R+r}$
Open section →3.4

Kirchhoff's Rules and the Wheatstone Bridge

Junction and loop rules, a method for any network, and the balance condition of the Wheatstone bridge.

$\sum I=0$, $\ \dfrac PQ=\dfrac RS$
Open section →
✅ Before you start
From Class 10 Physics, Chapter 3 (Electricity), you need current as rate of flow of charge, potential difference in volts, Ohm's law, resistors in series ($R=R_1+R_2+\cdots$) and in parallel ($1/R=1/R_1+1/R_2+\cdots$), and $P=VI$ — this chapter builds on all of them and does not repeat the series–parallel rules. From this course you need electric charge, conductors and the force $\mathbf F=q\mathbf E$ on a charge in a field (Section 1.1 and Section 1.2), and the idea of electric potential and potential difference from Chapter 2. From Class 11 Physics: kinematics with constant acceleration (for the drift of electrons) and work and energy. Kirchhoff's rules lead to two or three simultaneous linear equations, so be fluent at solving them.
← 2.4 Combinations of Capacitors and Stored Energy3.1 Electric Current, Drift Velocity and Ohm's Law →