The physics underneath engineering: electric circuits, forces and motion, and how energy moves and gets lost. Press play on any sketch to watch it happen.
1 Electric circuits
Voltage pushes, current flows, and resistance opposes. Ohm's law links the three, and Kirchhoff's laws let you work out any circuit. Every electronics project on this site relies on them.
Ohm's law: V = I × R.
Voltage law: all the voltage drops around a closed loop add up to the supply.
Current law: the current entering a junction equals the current leaving it.
Power: P = V × I, which is why resistors get warm.
I = V / R = 9 V / 3 kΩ = 3 mA
V1 = 3 mA × 1 kΩ = 3 V
V2 = 3 mA × 2 kΩ = 6 V
3 V + 6 V = 9 V
Circuit diagram
1/5 Total resistance in series is 1 kΩ + 2 kΩ = 3 kΩ.
Rule of thumb: Series resistors add up. Parallel resistors give a total smaller than the smallest one.
2 Forces and motion
Mechanics starts from Newton's laws. If the forces on an object balance, its motion does not change. If they do not, it accelerates in the direction of the leftover force.
First law: no net force means no change in motion.
Second law: F = m × a. The net force sets the acceleration.
Third law: every force has an equal and opposite partner.
Free-body diagram: draw one object and every force on it before you do any maths.
F_net = 3000 N - 1000 N = 2000 N
a = F / m = 2000 / 1000 = 2 m/s²
Free-body diagram
1/6 Isolate the car and draw every force on it.
Rule of thumb: Always work with the net force, not just the biggest arrow.
3 Energy and efficiency
Energy is never created or destroyed, only converted, and each conversion loses some as heat. Tracking where it goes is how engineers find what to improve.
First law: energy in equals energy out plus energy stored.
Second law: heat spreads out, so no real machine is 100% efficient.
Power: energy per second, measured in watts.
Efficiency: useful output divided by total input.
Energy flow diagram
1/5 A power station starts with 100 units of chemical energy in fuel.
Rule of thumb: Multiply the efficiency of each stage. Three stages at 90% give only 73% overall.
