Direct Current Notes

Electricity involves charges in motion; electric current is the ordered flow of charges.
In conductors, electric current is due to electron flow.
Electrons move randomly without an electric field, but flow towards the positive terminal when a conductor is connected to a battery.
Conventional current is defined as the flow of positive charges.
I = \frac{Q}{t}
- I: Electric current (Ampere, A)
- Q: Charge (Coulomb, C)
- t: Time (second, s)
Current density (J) is the current flowing per unit cross-sectional area: J = \frac{I}{A}.
Drift velocity (v_d) is the average velocity of electrons in an electric field; it's opposite to the electric field direction.
I = nAev_d
- n: Free electron density
- A: Cross-sectional area
- e: Electron charge
- vd: Drift velocity

Ohm’s law: The potential difference across a metallic conductor is proportional to the current flowing through it at a constant temperature.
V = IR
- V: Voltage (V)
- I: Current (A)
- R: Resistance (Ω)
Resistance is the ratio of potential difference to current: R = \frac{V}{I}.
Resistivity (\rho) measures a material's resistance to electrical conduction: R = \frac{\rho l}{A}.
- \rho: Resistivity (Ω m)
- l: Length (m)
- A: Cross-sectional area (m^2)
Conductivity (\sigma) is the reciprocal of resistivity: \sigma = \frac{1}{\rho}.
V = El where E is the electric field.
E = \rho J

Resistance of metals generally increases with temperature due to increased collisions between electrons and vibrating metal atoms.
\rho = \rho_0(1 + \alpha \Delta T)
R = R_0(1 + \alpha \Delta T)
- \alpha: Temperature coefficient of resistivity
- \Delta T: Change in temperature (T - T_0)
- R_0: Initial resistance
- R: Final resistance