Electric Current and Ohm's Law
Drift velocity, mobility, resistance, resistivity and their temperature dependence. (Physics › Current Electricity, NEET UG syllabus.)
What is Electric Current and Ohm's Law?
The rate of flow of electric charge through a cross-section of a conductor.
Key formula / rule: Electric Current
Key points
- Define electric current, drift velocity, and mobility.
- Derive the relationship between current and drift velocity.
- State and apply Ohm's Law (V=IR).
- Define resistance and resistivity and explain their dependence on material properties and dimensions.
Common exam trap
Confusing drift velocity with the speed of electric signal propagation.
Definitions
- Term
Electric Current
- Meaning
The rate of flow of electric charge through a cross-section of a conductor.
- Term
Drift Velocity
- Meaning
The average velocity attained by charged particles, such as electrons, in a material due to an electric field.
- Term
Mobility
- Meaning
The magnitude of the drift velocity per unit electric field (μ = vd / E).
- Term
Ohm's Law
- Meaning
States that for a conductor at constant temperature, the current flowing through it is directly proportional to the potential difference across its ends (V ∝ I or V = IR).
- Term
Resistance
- Meaning
The opposition offered by a conductor to the flow of electric current. Its SI unit is Ohm (Ω).
- Term
Resistivity
- Meaning
An intrinsic property of a material that quantifies how strongly it resists electric current. Its SI unit is Ohm-meter (Ωm).
- Term
Conductivity
- Meaning
The reciprocal of resistivity, indicating a material's ability to conduct electric current. Its SI unit is Siemens per meter (S/m).
Learning objectives
Define electric current, drift velocity, and mobility.
Derive the relationship between current and drift velocity.
State and apply Ohm's Law (V=IR).
Define resistance and resistivity and explain their dependence on material properties and dimensions.
Analyze the temperature dependence of resistance and resistivity for different materials.
Solve numerical problems involving current, voltage, resistance, resistivity, and temperature effects.
Formulae
- Name
Electric Current
- Note
Rate of flow of charge
- Expression
I = Q/t
- Name
Drift Velocity
- Note
e = charge of electron, E = electric field, τ = relaxation time, m = mass of electron
- Expression
vd = (eEτ)/m
- Name
Relation between Current and Drift Velocity
- Note
n = number density of free electrons, A = cross-sectional area
- Expression
I = n A e vd
- Name
Current Density
- Note
Current per unit area
- Expression
J = I/A = n e vd
- Name
Mobility
- Note
Drift velocity per unit electric field
- Expression
μ = vd / E = (eτ)/m
- Name
Ohm's Law (Macroscopic)
- Note
V = potential difference, I = current, R = resistance
- Expression
V = IR
- Name
Resistance
- Note
ρ = resistivity, L = length, A = cross-sectional area
- Expression
R = ρ (L/A)
- Name
Resistivity
- Note
Intrinsic property of the material
- Expression
ρ = m / (n e² τ)
- Name
Conductivity
- Note
Reciprocal of resistivity
- Expression
σ = 1/ρ = (n e² τ)/m
- Name
Ohm's Law (Microscopic)
- Note
Relates current density (J) and electric field (E)
- Expression
J = σE or E = ρJ
- Name
Temperature Dependence of Resistance
- Note
RT = resistance at T, R0 = resistance at T0, α = temperature coefficient of resistance
- Expression
RT = R0 [1 + α (T - T0)]
Prerequisites
Basic understanding of electric charge and its properties.
Concept of electric field and electric potential.
Knowledge of potential difference.
Common mistakes
Confusing drift velocity with the speed of electric signal propagation.
Applying Ohm's Law to non-ohmic devices (e.g., diodes, transistors).
Forgetting the temperature dependence of resistance/resistivity, especially for metals vs. semiconductors.
Mixing up resistance (property of object) and resistivity (property of material).
Incorrectly using units in calculations (e.g., cm instead of m).
Keywords
Electric current
Drift velocity
Mobility
Ohm's Law
Resistance
Resistivity
Conductivity
Temperature dependence
Charge carriers
Relaxation time
Practice preview
A resistor has a resistance of 10 Ohm. If a voltage of 20 V is applied across it, what is the current flowing through the resistor?…
easy
For a metallic conductor, how does its resistance change with an increase in temperature?…
medium
A wire of resistance R is stretched to twice its original length. Assuming its volume remains constant, what will be its new resistance?…
medium