Electric Current — Revision Notes

⚡ 30-Second Revision

Definition: — Rate of flow of charge, $I = \frac{dQ}{dt}$.
Unit: — Ampere (A), $1,\text{A} = 1,\text{C/s}$.
Charge Quantization: — $Q = Ne$, where $e = 1.6 \times 10^{-19},\text{C}$.
Microscopic Current: — $I = n A v_d e$.
Current Density: — $\vec{J} = \frac{I}{A} \hat{n}$ (vector), $J = n e v_d$.
Drift Velocity: — $v_d = \frac{eE\tau}{m_e}$.
Mobility: — $\mu = \frac{v_d}{E} = \frac{e\tau}{m_e}$.
Microscopic Ohm's Law: — $\vec{J} = \sigma \vec{E}$, where $\sigma = n e \mu = \frac{n e^2 \tau}{m_e}$ (conductivity).
Conventional Current: — Direction of positive charge flow (opposite to electron flow).
Nature of Current: — Scalar quantity.

2-Minute Revision

Electric current is the flow of electric charge, measured in Amperes ($1,\text{A} = 1,\text{C/s}$). The fundamental formula is $I = \frac{dQ}{dt}$. In metals, free electrons are the charge carriers. When an electric field is applied, these electrons acquire a small average velocity called drift velocity ($v_d$), which is opposite to the electric field.

The current is related to drift velocity by $I = n A v_d e$, where $n$ is the number density of electrons, $A$ is the cross-sectional area, and $e$ is the elementary charge. Current density ($vec{J}$) is current per unit area ($J = I/A$) and is a vector quantity, unlike current itself, which is a scalar.

Conventional current flows from high to low potential, opposite to electron flow. Remember to convert units (e.g., minutes to seconds, $mm^2$ to $m^2$) in numerical problems and be aware of the common misconception that drift velocity is fast; it is the electric signal that propagates quickly.

5-Minute Revision

To ace questions on Electric Current, start with the core definition: $I = \frac{dQ}{dt}$. This means current is the amount of charge passing a point per unit time. Remember the SI unit, Ampere, which is $1,\text{C/s}$. A common problem type involves calculating the number of electrons ($N$) flowing: $Q = Ne$, so $I = \frac{Ne}{t}$. For example, if $3.2,\text{A}$ flows for $10,\text{s}$, $Q = 32,\text{C}$, and $N = \frac{32}{1.6 \times 10^{-19}} = 2 \times 10^{20}$ electrons.

Next, delve into the microscopic picture. In conductors, free electrons move randomly. An applied electric field gives them a net average velocity called drift velocity ($v_d$), which is very small (e.

g., $10^{-4},\text{m/s}$). The key formula connecting macroscopic current to microscopic parameters is $I = n A v_d e$, where $n$ is the number density of charge carriers, $A$ is the cross-sectional area, and $e$ is the elementary charge.

For instance, if $n = 8 \times 10^{28},\text{m}^{-3}$, $A = 10^{-6},\text{m}^2$, and $I = 1.28,\text{A}$, then $v_d = \frac{I}{nAe} = \frac{1.28}{(8 \times 10^{28})(10^{-6})(1.6 \times 10^{-19})} = \frac{1.

28}{12.8} \times 10^{-3} = 0.1 \times 10^{-3} = 10^{-4}, ext{m/s}$.

Current density ($vec{J}$) is another important concept, defined as $J = I/A$. It's a vector, unlike current. Its unit is $A/m^2$. Also, remember the relationship $J = n e v_d$. The drift velocity is proportional to the electric field ($v_d = \mu E$), where $\mu$ is mobility. This leads to the microscopic form of Ohm's law: $\vec{J} = \sigma \vec{E}$, where $\sigma = n e \mu$ is conductivity.

Crucial conceptual points: Current is a scalar (adds algebraically). Conventional current (positive charge flow) is opposite to electron flow. The electric signal propagates at light speed, not the electrons themselves. Always ensure units are consistent (SI units) and practice handling powers of ten carefully.

Prelims Revision Notes

1
Definition of Current: — Electric current ($I$) is the rate of flow of electric charge ($Q$) through a conductor. $I = \frac{dQ}{dt}$. For average current, $I_{avg} = \frac{Delta Q}{Delta t}$.
2
Units: — SI unit of current is Ampere (A). $1,\text{A} = 1,\text{Coulomb/second} = 1,\text{C/s}$.
3
Charge Quantization: — Total charge $Q = Ne$, where $N$ is the number of charge carriers and $e = 1.6 \times 10^{-19},\text{C}$ is the elementary charge.
4
Number of Electrons: — If current $I$ flows for time $t$, then $Q = It$, and $N = \frac{It}{e}$.
5
Charge Carriers: — In metals, free electrons. In electrolytes, ions. In semiconductors, electrons and holes.
6
Drift Velocity ($v_d$): — The average velocity of charge carriers in the presence of an electric field. It's typically very small ($mm/s$).
7
Relation between Current and Drift Velocity: — $I = n A v_d e$, where $n$ is the number density of charge carriers (number per unit volume), $A$ is the cross-sectional area of the conductor, $v_d$ is the drift velocity, and $e$ is the charge of a single carrier.
8
Current Density ($vec{J}$): — Current per unit cross-sectional area. $\vec{J} = \frac{I}{A} \hat{n}$. It is a vector quantity, its direction is the direction of conventional current. Unit: $A/m^2$. Also, $J = n e v_d$.
9
Mobility ($\mu$): — Drift velocity per unit electric field. $\mu = \frac{v_d}{E}$. Unit: $m^2/(Vs)$.
10
Relaxation Time ($\tau$): — Average time between successive collisions of an electron with the lattice ions. $v_d = \frac{eE\tau}{m_e}$.
11
Microscopic Ohm's Law: — $\vec{J} = \sigma \vec{E}$, where $\sigma = n e \mu = \frac{n e^2 \tau}{m_e}$ is the electrical conductivity.
12
Conventional Current vs. Electron Flow: — Conventional current is the flow of positive charge (high to low potential). Electron flow is the actual movement of electrons (low to high potential). They are opposite.
13
Nature of Current: — Electric current is a scalar quantity. It does not obey vector addition laws.
14
Speed of Signal vs. Drift Speed: — The electric signal propagates at nearly the speed of light, while individual electrons drift very slowly. This is a key conceptual distinction.

Vyyuha Quick Recall

In New Age Video Editing: I = n A v_d e (Current = number density x Area x drift velocity x elementary charge). This helps recall the microscopic formula for current.