Electrical Circuits — Ohm's Law and Linear Equations
Electrical Engineering
Every electronic device — from your phone to a power grid — runs on equations so simple they're taught in algebra class.
$$V = IR$$
where $V$ = voltage (volts), $I$ = current (amps), $R$ = resistance (ohms, Ω).
This is $y = mx$ — a linear equation through the origin.
Series and Parallel Circuits
Series (resistors in a line):
$$R_{\text{total}} = R_1 + R_2 + R_3 + \cdots$$
This is simple addition.
Parallel (resistors side by side):
$$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots$$
This requires fractions — finding common denominators and reciprocals.
Two resistors, $R_1 = 100\,\Omega$ and $R_2 = 200\,\Omega$, are connected in parallel to a 12V battery. Find the total resistance and current.
Total resistance:
$$\frac{1}{R_T} = \frac{1}{100} + \frac{1}{200} = \frac{2}{200} + \frac{1}{200} = \frac{3}{200}$$
$$R_T = \frac{200}{3} \approx 66.7\,\Omega$$
Current (Ohm's law):
$$I = \frac{V}{R_T} = \frac{12}{66.7} \approx 0.18 \text{ A} = 180 \text{ mA}$$
Power consumed:
$$P = IV = 0.18 \times 12 = 2.16 \text{ W}$$
Power — Another Simple Equation
$$P = IV = I^2R = \frac{V^2}{R}$$
Power is voltage × current, or current² × resistance. These are the formulas that electrical engineers use to design everything from phone chargers to power plants.
Ohm's law ($V = IR$) is a linear equation. Parallel resistance uses fractions. Power uses squares. Every circuit in the world is designed with the same math you learn in algebra class.