Electric Current
1. What This Chapter Covers
You already know that lightning is an electric discharge between two clouds, or between a cloud and the Earth, and that it is direct evidence for the motion of charge in the atmosphere. The chapter's first question is sharper: does the motion of charge always lead to electric current?
Activity 1 answers it with three situations, using a bulb, a battery, a switch and insulated copper wires:
| Situation | Circuit | Does the bulb glow? |
|---|---|---|
| 1 | Battery, bulb, switch, copper wires | Yes |
| 2 | Battery removed, everything else connected | No |
| 3 | Battery present, but nylon wires instead of copper | No |
Situation 3 is the interesting one. A battery is present, yet nothing happens, because the nylon wires cannot carry the energy from the source to the bulb. So the nature of the substance matters:
A conductor transfers energy from the battery to the bulb. A non-conductor cannot.
Drude and Lorentz, at the beginning of the twentieth century, proposed the explanation: conductors like metals contain a large number of free electrons, while the positive ions are fixed in their places.
Consider a conductor in an open circuit. The free electrons move randomly, in any direction. Take any cross section: the number of electrons crossing it left to right in one second equals the number crossing right to left. So the net charge crossing any cross section is zero.
Connect the ends to a battery and the bulb glows, which means energy is being transferred. For the electrons to do that, their motion must become ordered — and then there is a net charge crossing every cross section.
Electric current is the ordered motion of charges.
The chapter is allotted 10 periods across October and November and runs from textbook page 176 to page 208.
2. Electric Current and Its Unit
Electric current is the amount of charge crossing any cross section of the conductor in one second.
If a charge Q crosses a cross section in time t, then
I = Q / t
The SI unit is the ampere, denoted A.
1 ampere = 1 coulomb / 1 second, that is 1 A = 1 C/s
The book gives the electron count for a coulomb: 1 coulomb = 6.625 × 10¹⁸ electrons.
Current is measured with an ammeter, which is always connected in series with the circuit. A multimeter set to its current range will do the same job.
3. Drift Speed, and Why It Is So Slow
When the conductor is connected to a battery the free electrons are accelerated towards the positive terminal. But they do not simply speed up forever. They collide with the positive ions, lose energy, may even come to a halt, are accelerated again by the field, collide again, and so on down the conductor.
The result of that repeated stop-start is a constant average speed, called the drift speed or drift velocity.
Deriving the current from the drift speed
Take a conductor of cross sectional area A, with n charges per unit volume — the charge density — each carrying charge q, drifting at speed v_d.
- In one second, one charge covers a distance v_d.
- The volume swept in that second is therefore A v_d.
- The number of charges in that volume is n A v_d.
- The total charge crossing the cross section in one second is n q A v_d.
That is the current:
I = n q A v_d ... (1)
v_d = I / (n q A) ... (2)
The number that surprises everyone
Put in real values for copper: a current of 1 A, a cross sectional area of 10⁻⁶ m², electron charge e = 1.602 × 10⁻¹⁹ C and the experimentally measured electron density of copper n = 8.5 × 10²⁸ m⁻³.
v_d = 1 / (8.5 × 10²⁸ × 1.6 × 10⁻¹⁹ × 10⁻⁶) = 7 × 10⁻⁵ m/s = 0.07 mm/s
The electrons are moving very slowly indeed — seven hundredths of a millimetre per second.
So why does a lamp light the instant you press the switch? Because the electrons do not have to travel from the switch to the lamp. When the circuit is closed, an electric field is set up throughout the conductor instantaneously, whatever the length of the wire, and that field makes all the electrons everywhere start moving in the specified direction at the same moment.
The direction of current
In I = n q A v_d, both n and A are positive, so the direction is decided by the signs of q and v_d.
For electrons, q is negative and v_d is positive, so the product is negative — meaning the direction of current is opposite to the flow of negative charge. For positive charges the product is positive. Hence:
The direction of electric current is taken as the direction of flow of positive charges.
4. Potential Difference
Where do the electrons get the energy for this motion?
When the ends of a conductor are joined to a battery, an electric field is set up throughout it, and that field exerts a force F_e on each free charge q. The field therefore does work to move charges in a specified direction.
If the charge moves a distance l from A to B, then since work is force times distance along the force,
W = F_e l
and the work done on unit charge is W/q = F_e l / q.
The potential difference between two points is the work done by the electric force on unit positive charge to move it from one point to the other.
V = W / q = F_e l / q
Potential difference is also called voltage. Its SI unit is the volt:
1 volt = 1 joule / 1 coulomb, that is 1 V = 1 J/C
Do positive charges ever move?
In metals, no — the positive ions are fixed in the lattice and only electrons move. But recall electrolysis and electroplating. In an electrolyte the positive ions (cations) and negative ions (anions) move in opposite directions, so conduction in fluids involves both.
Following the signs through: if positive charges move from A to B the electric field does positive work, so A is at high potential and B at low potential. Since negative charges move opposite to the field, electrons move from low potential to high potential.
5. How a Battery Holds Its Potential Difference Steady
A battery is two metal plates (electrodes) with a chemical (electrolyte) between them. The electrolyte contains positive and negative ions, and it exerts a chemical force F_c that drives them in opposite directions.
The sequence is a competition between two forces:
- Positive ions move to one plate and accumulate, making it positively charged — the anode. Negative ions accumulate on the other plate, making it the cathode.
- Once enough charge has piled up, the accumulated charge exerts an electric force F_e on the ions, opposite in direction to F_c and growing with the accumulated charge.
- Ions keep moving as long as F_c is stronger than F_e.
- Accumulation stops when F_e becomes equal to F_c. The forces are balanced and the ions stop moving.
A new battery bought from the shop is at exactly this balanced stage — and that balance is the reason the potential difference between its terminals is constant. How much charge accumulates depends on the chemical used.
What happens when the battery is connected
Connecting a conducting wire creates a potential difference across the conductor and sets up a field in it, directed from the positive terminal to the negative terminal.
Electrons near the positive terminal are attracted to it and move towards it. The positive plate's charge therefore falls, F_e becomes weaker than F_c, and the chemical force resumes pulling negative ions from the anode towards the cathode. The negative terminal then pushes one electron into the conductor, by repulsion.
Two things follow. The total number of electrons in the conductor stays constant during current flow, and the process continues until equilibrium between F_e and F_c is reached again.
6. Electromotive Force
While electrons drift from the negative terminal to the positive terminal in the external conductor, inside the battery negative ions of equal charge are moved from the positive terminal to the negative terminal against the electric force, by the chemical force. Chemical energy is being spent, so work is being done.
If the terminals are a distance d apart and the chemical force does work W = F_c d on a charge q, and taking F_c = F_e at balance, the work done per coulomb is
ε = W / q = F_e d / q
emf is the work done by the chemical force to move unit positive charge from the negative terminal to the positive terminal of the battery.
Potential difference and emf are both measured with a voltmeter, which must be connected in parallel across the device.
7. Ohm's Law
The lab activity
Aim: to show that the ratio V/I is constant for a conductor.
Materials: 5 dry cells of 1.5 V each, conducting wires, an ammeter, a voltmeter, a thin iron or manganin spoke 10 cm long, an LED and a key.
Procedure: solder the wires to the ends of the iron spoke and close the key with one cell. Record the current and the potential difference. Repeat with two cells in series, then three, four and five, recording V and I each time, and compute V/I for every pair.
Result: the ratio V/I is a constant. Plotting I against V gives a straight line through the origin.
Now repeat the whole thing with an LED in place of the spoke, connecting its long terminal to the positive and short terminal to the negative. This time V/I is not constant and the graph is a curve.
The law
The result for the spoke was established by the German physicist George Simon Ohm:
The potential difference between the ends of a conductor is directly proportional to the electric current passing through it, at constant temperature.
V ∝ I (temperature constant), so V / I = R, giving V = I R
R is the resistance. Its SI unit is the ohm, symbol Ω:
1 ohm = 1 volt / 1 ampere, that is 1 Ω = 1 V/A
Materials split into two classes on this test. Ohmic materials obey the law — metals. Non-ohmic materials do not — LEDs.
Limitations of Ohm's law
- Valid for metal conductors only while temperature and other physical conditions stay constant. Resistance changes with temperature, so a changing-temperature V-I graph is non-linear.
- Not applicable to gaseous conductors.
- Not applicable to semiconductors such as germanium and silicon.
What resistance actually is
When the conductor is connected, electrons drift, collide with the fixed positive lattice ions, and lose mechanical energy as heat. The field restores their energy and they move on. The lattice ions obstruct the motion, and how much they obstruct it depends on the material.
Resistance is the obstruction to the motion of electrons in a conductor, and a material that offers it is a resistor.
8. Electric Shock
Treat the human body as a resistor. Its resistance ranges from 100 Ω when wet with salt water to 5,00,000 Ω when the skin is very dry.
Suppose you touch both terminals of a 24 V battery with dry fingers, with a body resistance of 1,00,000 Ω:
I = 24 / 100000 = 0.00024 A
That current is far too small to disturb any organ. Now touch a live wire of 240 V:
I = 240 / 100000 = 0.0024 A
At this level the functioning of organs is disturbed, and that disturbance is what you feel as electric shock. If the current continues, it damages tissue, which lowers body resistance, which raises the current further — a feedback that makes a long contact far more dangerous than a brief one.
Table-2 gives the thresholds:
| Current (A) | Effect |
|---|---|
| 0.001 | Can be felt |
| 0.005 | Is painful |
| 0.010 | Causes involuntary muscle contractions (spasms) |
| 0.015 | Causes loss of muscle control |
| 0.070 | If through the heart, causes serious disruption; probably fatal if it lasts more than one second |
So a shock needs a potential difference between one part of the body and another. Current takes the path of least resistance, and resistance is not uniform — skin offers more resistance than the organs inside. Shock is therefore a combined effect of potential difference, current and the body's resistance.
Why the bird on the high voltage wire is safe
There are two parallel transmission lines on the poles, with 240 V between them along their whole length. Connect any conducting device across the two and current flows. But a bird sitting on a single wire has no potential difference between its legs, so no current passes through it and it feels nothing.
9. What Resistance Depends On
Four activities, each isolating one variable.
Activity 2 - temperature. Measure a bulb's resistance in open circuit with a multimeter set to ohms at 20 kΩ. Then connect the bulb in a circuit, switch on, wait a few minutes and measure again. The second reading is higher. The filament has heated up. Resistance increases with rise in temperature.
The Do you know? box describes the instrument: a multimeter combines several measurement functions in one unit, with a display of about four digits, a selection knob for mA, V and Ω, and two ports — COM for the black lead and mAVΩ for the red.
If the meter reads 1 or OL it is overloaded and you need a higher range such as 200 kΩ or 2 MΩ; if it reads 0.00 you need a lower range. The box carries a warning: most multimeters can measure AC, but AC circuits can be dangerous, so measure DC only.
Activity 3 - material. Take rods of copper, aluminium and iron, all the same length and same cross section, and connect each in turn between P and Q in the circuit. The currents differ. Resistance depends on the material.
Activity 4 - length. Take iron spokes of different lengths and the same cross section. The current decreases as the spoke gets longer:
R ∝ l (at constant temperature and cross section) ... (1)
Activity 5 - cross section. Take iron rods of equal length and different cross sections. The current increases with cross sectional area:
R ∝ 1/A (at constant temperature and length) ... (2)
Combining (1) and (2):
R ∝ l/A, so R = ρ l / A
The constant ρ is the specific resistance or resistivity. Its SI unit is Ω m, and its reciprocal is the conductivity σ.
The distinction to hold on to: resistivity depends only on the temperature and the nature of the material, while resistance also depends on the geometry — the length and the cross section.
Table 3: resistivity of various materials, in Ω m at 20 °C
| Material | ρ | Material | ρ |
|---|---|---|---|
| Silver | 1.59 × 10⁻⁸ | Nichrome | 1.10 × 10⁻⁶ |
| Copper | 1.68 × 10⁻⁸ | Carbon (graphite) | 2.50 × 10⁻⁶ |
| Gold | 2.44 × 10⁻⁸ | Germanium | 4.60 × 10⁻¹ |
| Aluminium | 2.82 × 10⁻⁸ | Drinking water | 2.00 × 10⁻¹ |
| Calcium | 3.36 × 10⁻⁸ | Silicon | 6.40 × 10² |
| Tungsten | 5.60 × 10⁻⁸ | Wet wood | 1.00 × 10³ |
| Zinc | 5.90 × 10⁻⁸ | Glass | 10.0 × 10¹⁰ |
| Nickel | 6.99 × 10⁻⁸ | Rubber | 1.00 × 10¹³ |
| Iron | 1.00 × 10⁻⁷ | Air | 1.30 × 10¹⁶ |
| Lead | 2.20 × 10⁻⁷ |
The table explains a string of everyday choices. Copper has low resistivity, so it is used for wires. The bulb filament is tungsten, chosen for its higher resistivity and its melting point of 3422 °C. Insulators run from 10¹⁴ to 10¹⁶ Ω m.
Alloys deserve their own note. Nichrome (nickel, chromium and iron) and Manganin (86 per cent copper, 12 per cent manganese, 2 per cent nickel) have 30 to 100 times the resistivity of metals, which suits them to the heating elements of electric irons and toasters. They have two further advantages: their resistance varies very little with temperature, and they do not oxidise easily.
Semiconductors such as silicon and germanium are 10⁵ to 10¹⁰ times more resistive than metals but 10¹⁵ to 10¹⁶ times less resistive than insulators, and they are used to make diodes, transistors and integrated circuits.
10. Series and Parallel Combinations
A circuit is a closed path through which electrons can flow. For continuous flow it must be complete, with no gaps — the gap deliberately provided by a switch is what lets you cut off the current.
In a series connection there is a single path between the terminals. In a parallel connection the components form branches, each a separate path.
Series
Activity 6 measures three bulbs' resistances as R₁, R₂ and R₃, connects them in series, and measures the potential difference across each and across the battery. The result:
V = V₁ + V₂ + V₃ ... (1)
The current is the same everywhere, because there is only one path. By Ohm's law V₁ = IR₁, V₂ = IR₂, V₃ = IR₃, and for the equivalent resistance V = I R_eq.
Equivalent resistance is the resistance that would draw the same current as the combination, from the same source.
Substituting into (1): I R_eq = I R₁ + I R₂ + I R₃, so
R_eq = R₁ + R₂ + R₃
What happens if one resistor in a series breaks? The circuit becomes open and no current flows anywhere. This is exactly why household appliances are not connected in series.
Parallel
Activity 7 reconnects the same bulbs in parallel. The potential difference across each bulb is the same, and the current drawn from the battery equals the sum of the individual currents:
I = I₁ + I₂ + I₃ ... (1)
With I₁ = V/R₁, I₂ = V/R₂, I₃ = V/R₃ and I = V/R_eq:
1/R_eq = 1/R₁ + 1/R₂ + 1/R₃
For two resistors this rearranges to R_eq = R₁R₂ / (R₁ + R₂).
The equivalent resistance of a parallel combination is less than every one of the individual resistances. The book uses that result to explain something from the previous section: imagine a thick wire as several thin wires in parallel. The combination has less resistance than any one thin wire — which is why resistance is inversely proportional to cross sectional area.
The book's worked examples
| Example | Given | Working | Answer |
|---|---|---|---|
| 1(a) | 10, 20, 30 Ω in series | 10 + 20 + 30 | 60 Ω |
| 1(b) | 10, 20, 30 Ω in parallel | 1/R = 1/10 + 1/20 + 1/30 = 11/60 | 5.5 Ω |
| 2 | R₁, 4 Ω, 8 Ω in series give 20 Ω | 20 = R₁ + 12 | R₁ = 8 Ω |
| 3 | R₁ and 12 Ω in parallel give 3 Ω | 1/R₁ = 1/3 − 1/12 = 3/12 | R₁ = 4 Ω |
| 4 | 4 Ω parallel 12 Ω, then 7 Ω in series | 48/16 = 3, then 3 + 7 | 10 Ω |
11. Kirchhoff's Laws
Replacing series and parallel groups by their equivalents is useful, but not sufficient for circuits containing more than one battery. Two rules apply to any DC circuit of batteries and resistors, however connected.
Junction law
A junction is a point where three or more conducting wires meet.
At any junction, the sum of the currents into the junction equals the sum of the currents leaving it.
For the book's fig-23 that reads I₁ + I₄ + I₆ = I₅ + I₂ + I₃. The physical content is that there is no accumulation of charge at any junction, so the law rests on the conservation of charge.
Loop law
The algebraic sum of the increases and decreases in potential difference across the components of a closed loop must be zero.
Travel right round a loop measuring the change at each component; when you arrive back at the start, the net change must be zero, because you are back at the same potential. This law rests on the conservation of energy.
The sign convention
| Moving | Sign |
|---|---|
| Across a battery from positive terminal to negative terminal | emf taken negative |
| Across a battery from negative terminal to positive terminal | emf taken positive |
| Through a resistor along the current direction | potential difference taken negative |
| Through a resistor against the current direction | potential difference taken positive |
Applying it to a single-battery single-resistor loop gives −V₁ + I R₁ = 0. For a loop with two batteries and three resistors, I R₁ + I R₂ − V₁ + I R₃ − V₂ = 0.
Example 6 is the one worth practising. A 12 V battery and a 5 V battery sit in a network of 2 Ω, 3 Ω and 4 Ω. Distributing the currents by the junction law and applying the loop law twice:
- Loop DAFED:
−3I₁ + 12 − 4I = 0, so4I + 3I₁ = 12 - Loop DABCD:
−3I₁ + 12 − 5 + 2(I − I₁) = 0, so2I − 5I₁ = −7
Solving the pair gives I₁ = 2 A, the current drawn from the 12 V battery.
12. Electric Power and Electric Energy
Let a charge Q pass from A to B in t seconds through a conductor with potential difference V between those points. The work done by the electric field is
W = Q V ... (1)
and this is the energy the charge loses in passing through. Dividing by t:
W/t = (Q/t) V ... (2)
Here Q/t is the current I, and W/t — work done per second — is the electric power P:
P = V I ... (3)
Using V = IR, the same power can be written two other ways:
P = I² R = V² / R
For a source rather than a device, the same relation becomes P = ε I, with ε the emf.
Reading the marking on a bulb
A bulb marked 60 W and 120 V will convert 60 joules of electrical energy into heat or light every second when connected to a 120 V source. Its resistance follows from P = V²/R:
R = V²/P = (120 × 120) / 60 = 240 Ω
Connect that same bulb to a 12 V battery instead and its consumption is
P = V²/R = (12 × 12) / 240 = 0.6 W
The unit on your electricity bill
Watt is a small unit, so power is usually expressed in kilowatts: 1 kW = 1000 W = 1000 J/s.
The "unit" on a domestic bill is 1 kilowatt hour:
1 kWh = (1000 J/s) × (60 × 60 s) = 3600 × 1000 J = 3.6 × 10⁶ J
13. Overloading and the Fuse
Electricity enters a house through two low-resistance line wires with about 240 V between them. Every appliance is connected between these two wires, which means all household appliances are in parallel, and each has the full 240 V across it. The current each draws follows from I = V/R — a 240 Ω bulb draws exactly 1 A.
By the junction law, the total current from the mains is the sum of the currents through all the devices, so adding appliances raises the total.
The domestic meter is marked with its limits:
- Potential difference: 240 V
- Current: 5-20 A
So the maximum you may draw is 20 A. Draw more and overheating occurs and may cause a fire — this is overloading. The book's fig-32 totals a TV at 6 A, a fridge at 8 A, a bulb at 2 A, a fan at 4 A and a heater, which together push past the limit.
The protection is an electric fuse in the household circuit, arranged so that all the current from the mains passes through it. The fuse is a thin wire of low melting point. When the current exceeds 20 A the wire heats and melts, the circuit opens, and every device is saved.
The book adds a note: the overload current is not a universal number — it varies from household circuits to factories.
The Think and discuss box here asks two questions worth writing out: what a short circuit is, and why it damages wiring and the devices connected to it.
14. Annexure: Ohm's Law from Newton's Second Law
The annexure asks whether Newton's laws can be applied to electrons, and derives Ohm's law from them, neglecting random motion.
For a conductor of length l, area A and electron density n:
I = n A e v_d ... (a)
The work done by the source to move one electron between the ends is W = V e ... (b), and the work done by the electric force is W = F l ... (c). From (b) and (c), F = V e / l.
By Newton's second law F = ma, so a = V e / l m ... (d).
Take the initial velocity as zero and let τ be the interval between successive collisions. Then v = a τ = V e τ / l m. Because collisions restrict the motion, the average velocity over τ is the drift velocity:
v_d = (v + u)/2 = v/2 = V e τ / 2 l m
Substituting in (a):
I = n A e (V e τ / 2 l m), so I (2m / n e² τ)(l / A) = V ... (e)
Now look at what is constant. The mass and charge of the electron are fixed. The electron density n is fixed for a given material. The length l and area A are fixed for a given conductor. τ depends on temperature — a higher temperature means more random motion and a smaller τ — but at constant temperature τ is constant too.
So the whole bracket is a constant for a given conductor at a given temperature. Call it R:
I R = V ... (f)
which is Ohm's law, with
R = (2m / n e² τ)(l / A) ... (g)
The first factor depends only on the material, not the geometry, so it is the specific resistance:
ρ = 2m / n e² τ, giving R = ρ l / A ... (h)
This derivation also explains the temperature dependence found in Activity 2: heating the conductor shortens τ, which raises ρ and therefore raises R.
Key words from the chapter
Charge, potential difference, electric current, multimeter, Ohm's law, resistance, resistivity, Kirchhoff's laws, electric power, electric energy.
15. Summary
Current is the ordered motion of charges, I = Q/t, measured in amperes with an ammeter in series; 1 C = 6.625 × 10¹⁸ electrons. In an open circuit the free electrons move randomly and the net charge crossing any cross section is zero.
The drift picture gives I = n q A v_d, and for 1 A in a copper wire of 10⁻⁶ m² the drift speed is only 0.07 mm/s. The lamp still lights instantly, because closing the switch sets up the field along the whole conductor at once. Since the carriers are electrons, the conventional current direction is opposite to their motion.
Potential difference is the work done by the electric force on unit positive charge, V = W/q, in volts, where 1 V = 1 J/C. emf is the work done by the chemical force per unit charge inside the battery, and a battery holds a steady terminal voltage because the chemical force and the electric force are in balance.
Ohm's law, V = IR, holds for metals at constant temperature. The iron spoke gives a straight line through the origin; the LED gives a curve, and is non-ohmic. The law fails for gaseous conductors and for semiconductors. Resistance is the obstruction to electron motion by the lattice ions.
Resistance rises with temperature and with length, falls with cross sectional area, and depends on the material: R = ρ l / A. Resistivity is a property of the material alone, in Ω m; copper's low value suits it to wires, tungsten's higher value plus a 3422 °C melting point suits it to filaments, and nichrome and manganin at 30-100 times the resistivity of metals suit them to heating elements.
Resistors in series add, R_eq = R₁ + R₂ + R₃, and one failure opens the whole circuit. Resistors in parallel add as reciprocals, 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃, and the result is smaller than any single resistor — which is why households are wired in parallel.
Kirchhoff's junction law follows from conservation of charge and the loop law from conservation of energy, and between them they handle circuits with more than one battery.
Power is P = VI = I²R = V²/R, and the bill's "unit" is the kilowatt hour, 1 kWh = 3.6 × 10⁶ J. Since appliances are in parallel, the total current from the mains is the sum of all of them; exceeding the meter's 20 A limit is overloading, and a fuse of thin low-melting-point wire breaks the circuit before the wiring catches fire.
Finally, the body's resistance runs from 100 Ω wet to 5,00,000 Ω dry. A 24 V battery gives a harmless 0.24 mA, a 240 V line gives 2.4 mA and a shock, and 0.07 A through the heart for more than a second is probably fatal. A bird on a single wire is safe because there is no potential difference between its feet.
