Electric Current

Electric current is the flow of charge, measured in amperes (A). It’s like water flowing through a pipe, but with electrons moving through a wire!

Resistance

Resistance is how much a material opposes current:

\[ R = \rho \frac{L}{A} \] where \( \rho \) is resistivity, \( L \) is length, and \( A \) is cross-sectional area.

Ohm’s Law

The relationship between current, voltage, and resistance is:

\[ V = IR \]

Series and Parallel Circuits

• Series: Current is the same, voltages add.
• Parallel: Voltage is the same, currents add.

Calculus in Circuits

Charge and current can change with time, so we use derivatives and integrals to analyze RC, RL, and RLC circuits.

Real-World Example

Understanding circuits keeps your phone from overheating and helps engineers design safe power systems.