Electric Current

1.0Electric Current Definition

Electric current is defined as the rate of flow of electric charge through a cross-section of a conductor. In a metallic conductor, these charge carriers are free electrons. The electrical current formula for the average current $(I_{\text{avg}})$ is:

$I_{\text{avg}}=\frac{\Delta Q}{\Delta t}$

where ΔQ is the net charge that flows through a surface in a time interval Δt. For instantaneous current, we use the derivative:

$I=\frac{dQ}{dt}$

The electrical current symbol is I.

$\text{Area}={\int }_{t_1}^{t_2}Idt=\Delta q$

Direction of current is along the direction of flow of positive charge or opposite to the direction of flow of negative charge. But the current is a scalar quantity.

Current Flow Essentials

For an electric current to flow, two conditions must be met:

1. Presence of Free Charge Carriers: The material must contain mobile charge carriers, such as free electrons in metals or ions in electrolytes.
2. Potential Difference: There must be a potential difference (voltage) across the conductor. This difference creates an electric field that drives the charge carriers in a particular direction, giving them a net drift velocity.

Electro motive force (E.M.F.):

The potential difference across the terminals of a cell when it is not delivering any current is called emf of the cell. The energy given by the cell in the flow of unit charge in the whole circuit (including the cell) is called the emf of the cell.

• emf depends on:
  1. Nature of electrolyte
  2. Metal of electrodes
• emf does not depend on:
  1. Area of plates
  2. Distance between the electrodes
  3. Quantity of electrolyte
  4. Size of cell

2.0Unit of Electric Current

The SI unit of electric current is the ampere (A). The electrical current unit is named after André-Marie Ampère. One ampere is defined as the flow of one coulomb of charge per second.

$1\text{Ampere}=1\frac{\text{Coulomb}}{\text{second}}$

Smaller units like milliamperes (mA) and microamperes (μA) are commonly used in electronics.

3.0Types of Electric Current

There are two main types of electric current based on the direction of charge flow.

Direct Current (DC)

Direct Current (DC) is a type of current where the charge flows in only one direction. The magnitude of the current can be constant or can vary over time, but the direction remains the same. Batteries, solar cells, and fuel cells produce DC.

Alternating Current (AC)

Alternating Current (AC) is a type of current where the direction of charge flow reverses periodically. The magnitude of the current also changes continuously over time. AC is the type of current supplied to homes and businesses by power plants. Its waveform is typically a sine wave.

On the basis of nature

1. Average Electric Current

If Δq charge flows through a conductor in a time interval Δt, then the average current is given by:

$i_{\text{avg}}=\frac{\Delta q}{\Delta t}$

2. Instantaneous Current

The value of current at a particular instant of time is called instantaneous current. It is given by:

$i={\lim }_{\Delta t\to 0}\frac{\Delta q}{\Delta t}=\frac{dq}{dt}$

Also,

$dq=i,dt\text{or}q=\int i,dt$

4.0Types of Current Flow

The direction of current is defined as the direction of flow of positive charge. This is called conventional current. However, in most conductors (like metals), it is the negatively charged electrons that actually move. Therefore:

• Conventional Current flows from the positive terminal to the negative terminal of a battery.
• Electron Flow is from the negative terminal to the positive terminal.

If moving charges are negative, the current is opposite to the direction of motion of negative charges.

If the moving charges are positive, the current is in the direction of motion of positive charge.

Some important points about current

(1) Current is a fundamental quantity with dimensions [M⁰L⁰T⁰A¹]

(2) Current is a scalar quantity with its SI unit being ampere and it does not follow vector law of addition.

(3) Direction of current is in the direction of flow of positive charge or we can say opposite to the direction of flow of negative charge.

(4) Slope of q – t graph gives us current.

(5) Area under i–t curve gives us total charge flown.

Ampere: The current through any conductor is said to be one ampere if one coulomb of charge is flowing per second through any cross-section of the wire.

5.0Current Characteristics

• Scalar Quantity: Despite having a direction, electric current is a scalar quantity. It does not follow the laws of vector addition. For instance, currents entering a junction add algebraically, not vectorially.
• Drift Velocity: The actual speed of electrons (drift velocity) is very slow, typically on the order of millimeters per second. The electric field, however, propagates at nearly the speed of light, which is why an electrical device turns on instantly when a switch is flipped.
• Current Density (J): This is a vector quantity that describes the amount of current flowing per unit cross-sectional area. J= \frac{I}{A}

6.0Impact of Electric Current

Electric current has three main effects, which form the basis for many technologies.

Heating Effect of Electric Current

When current flows through a resistor, some of the electrical energy is converted into heat. This is due to the collisions of charge carriers with the atoms of the conductor. The heat produced (H) is given by Joule's Law of Heating:

$H=I^{2}Rt$

This effect is used in heaters, light bulbs, and fuses.

Magnetic Effect of Electric Current

A current-carrying conductor produces a magnetic field around it. The direction of this field can be determined by the right-hand thumb rule. The strength of the magnetic field is directly proportional to the current. This principle is the basis for electromagnets, electric motors, and generators.

Chemical Effect of Electric Current

When an electric current is passed through an electrolyte (a solution of ions), it can cause chemical reactions at the electrodes. This process is called electrolysis. It is used in electroplating, extraction of metals, and in charging batteries.

Problem 1:
A copper wire has a cross-sectional area of $1\times 10^{-6}{\text{m}}^2$ and carries a current of 2 A. If the number of free electrons per unit volume is$8.5\times 10^{28}{\text{m}}^{-3}$,  find the drift velocity of the electrons.

Solution:

$$\begin{gathered} \text{Using the formula}I=nAe{v}_d: \\ {v}_d=\frac{I}{nAe} \\ =\frac{2}{(8.5\times 10^{28})(1\times 10^{-6})(1.6\times 10^{-19})} \\ {v}_d\approx 1.47\times 10^{-4}\text{m/s} \end{gathered}$$

Problem 2:
A charge of 240 C flows through a wire in 2 minutes. What is the electric current in the wire?

Solution: 

$$\begin{gathered} Q=240\text{C} \\ t=2\text{minutes}=2\times 60=120\text{s} \\ I=\frac{Q}{t}=\frac{240}{120}=2\text{A} \end{gathered}$$

Problem 3:
Current I = (2 + 4t) A where t is in seconds, is flowing through a wire for 2 seconds. Find out the amount of charge flown through the wire.

Solution:

$q={\int }_0^{2}idt={\int }_0^2(2+4t)dt=12\text{C}$

Alternate method:
At t=0, I=2A and at t=2, I=10A

Area under i–t curve = total charge= $\frac{1}{2}(2+10)\times 2=12\text{C}$

Problem 4:
The current through a wire depends on time as $i=i_0+\alpha \sin (\pi t)where{i}_0=10\text{A}\text{and}\alpha =\frac{\pi }{2}\text{A}$. Find the charge crossed through a section of the wire in 3 seconds, and the average current for that interval.

Solution:

Average current is:

$$\begin{gathered} I=\frac{dq}{dt} \\ dq=idt \\ q={\int }_0^3\left(i_0+\alpha \sin (\pi t)\right)dt \\ ={\left[i_{0}t+\frac{\alpha }{\pi }(-\cos \pi t)\right]}_0^3 \\ q=3i_0+\frac{2\alpha }{\pi }=31\text{C} \\ \text{Average current is:} \\ {i}_{\text{avg}}=\frac{q}{\Delta t}=\frac{31\text{C}}{3\text{s}}=\frac{31}{3}\text{A} \end{gathered}$$