Electric Current in Conductors: Formula, Types and Examples
When you switch on a lamp, charge moves through the electrical circuit and the lamp lights up. This movement of electric charge is called electric current. In a metal wire, the moving charges responsible for conduction are mainly free electrons.
This lesson explains how current flows through a conductor, how it is calculated, what current density means, and how direct current (DC) differs from alternating current (AC).
1. How Does Electric Current Flow in a Conductor?
Metals such as copper and aluminium contain electrons that can move through the material. These are often called free electrons. Without an applied electric field, their motion is random, so there is no sustained net flow of charge through the wire.
When a potential difference is applied across the wire, an electric field is established inside it. The free electrons acquire a net drift opposite to the direction of that field. Their combined motion produces electric current.
Interactive SVG: See How Current Flows
Adjust the current, reverse its direction, or pause the animation. The arrows show conventional current and electron drift in a metal wire.
Conventional current: left · Electron drift: right · Selected current: 3 A
Learning model only: animation speed is illustrative and does not represent the actual microscopic drift speed of electrons. The slider changes the visual speed, not a measured circuit current.
The charges carrying current depend on the material. In metals, they are mainly electrons; in electrolytes, they are positive and negative ions. In semiconductors, both electrons and holes can contribute to conduction.
2. Electric Current Formula and SI Unit
Electric current tells us how quickly electric charge passes through a chosen cross-section of a conductor. If a charge Q passes through that cross-section in time t, the average current is:
Where:
- I = electric current, measured in amperes (A)
- Q = charge transferred, measured in coulombs (C)
- t = time taken, measured in seconds (s)
For current that changes with time, this formula gives the average current over the specified interval. The instantaneous current is defined by I = dQ/dt, with a consistent choice of current direction.
What is one ampere?
One ampere is the rate of charge flow of one coulomb per second through a cross-section.
For example, a current of 2 A means that 2 coulombs of charge pass a cross-section each second, on average.
3. Conventional Current and Electron Flow
Two directions are used when describing current in a metal conductor. It is important not to confuse them.
| Term | Direction in a metal wire | Meaning |
|---|---|---|
| Conventional current | From higher potential to lower potential through the external circuit | The direction assigned to positive charge flow |
| Electron flow | Opposite to conventional current | The net drift direction of electrons in the metal |
Conventional current is the standard direction used in circuit diagrams and electrical calculations. In a simple circuit powered by a battery, conventional current flows through the external circuit from the positive terminal toward the negative terminal.
4. Current Density: Formula, Unit and Meaning
Current density describes how much electric current passes through a unit area of a conductor's cross-section. It is useful when comparing wires of different thicknesses.
Where:
- J = average current density for a uniform current distribution
- I = current through the cross-section
- A = cross-sectional area of the conductor
The SI unit of current density is ampere per square metre (A/m²). Current density is a vector quantity; the formula above gives its magnitude when the current is uniformly distributed across the area.
A wire carries a current of 4 A and has a cross-sectional area of 2 × 10-6 m². Find its average current density.
Step 1: Write the formula
J = I / A
Step 2: Substitute the values
J = 4 / (2 × 10-6)
Step 3: Calculate
J = 2 × 106 A/m²
5. Types of Electric Current
Electric current is commonly classified into direct current (DC) and alternating current (AC), based on how its direction and magnitude behave over time.
Direct Current (DC)
Direct current flows in one direction. In steady DC, its magnitude also remains constant. However, DC does not have to be constant: a varying DC can change its magnitude while maintaining the same direction.
Examples: A battery supplying a simple circuit and a USB power supply delivering DC to a device.
Alternating Current (AC)
Alternating current periodically reverses direction. In a common sinusoidal AC supply, its magnitude changes continuously and its direction reverses during each cycle.
Household mains electricity is an example of AC. In India, the standard mains supply frequency is 50 Hz, meaning 50 complete cycles per second.
| Feature | Direct Current (DC) | Alternating Current (AC) |
|---|---|---|
| Direction | Does not reverse | Reverses periodically |
| Magnitude | May be constant or vary | Usually varies with time in common AC supplies |
| Frequency | Zero for steady DC; a varying DC signal can contain changes over time | Has a repetition frequency for periodic AC |
| Common example | Battery output | Household mains supply |
6. Solved Numerical Examples on Electric Current
Example 1: Find current from charge and time
A charge of 30 C passes through a wire in 10 seconds. Calculate the average current.
Formula: I = Q / t
Substitution: I = 30 / 10
Answer: I = 3 A
Example 2: Find the charge transferred
A steady current of 2 A flows for 15 seconds. How much charge passes through the wire?
From I = Q / t, rearrange to obtain Q = It.
Q = 2 × 15 = 30 C
Answer: 30 C
Example 3: Find the time taken
How long does a steady current of 5 A take to transfer 100 C of charge?
From I = Q / t, rearrange to obtain t = Q / I.
t = 100 / 5 = 20 s
Answer: 20 seconds
7. What Affects Electric Current in a Conductor?
In a simple DC circuit with an ohmic conductor at a fixed temperature, current depends on the applied voltage and the conductor's resistance.
Here, V is the potential difference in volts and R is the resistance in ohms.
- Applied voltage: Increasing the voltage increases the current if resistance remains constant.
- Resistance: Increasing resistance decreases current if the applied voltage remains constant.
- Wire length: For the same material, cross-sectional area and temperature, a longer wire generally has greater resistance.
- Cross-sectional area: A thicker wire generally has lower resistance than a thinner wire of the same material and length.
- Temperature: Resistance changes with temperature; for ordinary metallic conductors, it generally increases as temperature rises.
These relationships are useful for understanding why wires of different sizes are chosen for different electrical applications.
8. Frequently Asked Questions
What is electric current in a conductor?
Electric current is the rate at which electric charge passes through a cross-section of a conductor. In metals, current is associated with the net drift of free electrons.
What is the SI unit of electric current?
The SI unit is the ampere (A). One ampere is equivalent to one coulomb of charge passing per second.
What is the formula for electric current?
For average current, I = Q/t, where Q is the charge transferred and t is the time taken.
Why do electrons move opposite to conventional current?
Electrons carry negative charge. Their net drift in a metal wire is opposite to the conventional current direction, which is defined as the direction positive charge would move.
What is the difference between AC and DC?
DC does not reverse direction, whereas AC reverses direction periodically. The magnitude of DC can vary without changing its direction.
What is current density and its SI unit?
Current density describes current per unit cross-sectional area. For a uniform distribution, J = I/A. Its SI unit is A/m².
Can current flow without a complete circuit?
A sustained current in an ordinary closed conducting circuit requires a complete conducting path. Transient currents can occur briefly when charge redistributes, even before a steady circuit condition is established.
9. Test Your Understanding
Question: A current of 4 A flows through a wire for 5 seconds. How much electric charge passes through the wire?
- Electric current is the rate of flow of charge.
- The SI unit of current is the ampere.
- Average current: I = Q/t.
- Average current density for uniform current: J = I/A.
- DC maintains its direction; AC reverses direction periodically.
- Conventional current and electron drift in metals have opposite directions.