Voltage is the 'electrical pressure' that pushes current through a circuit. Think of it like water pressure in pipes. Higher voltage = stronger push. Measured in volts (V). Not the same as current or power!

• 1 volt = 1 joule per coulomb (energy per charge)
• Voltage causes current to flow (like pressure causes water flow)
• Measured between two points (potential difference)
• Higher voltage = more energy per charge

Voltage (V) = pressure, Current (I) = flow rate, Power (P) = energy rate. P = V × I. 12V at 1A = 12W. Same power, different voltage/current combos possible.

• Voltage = electrical pressure (V)
• Current = flow of charge (A)
• Power = voltage × current (W)
• Resistance = voltage ÷ current (Ω, Ohm's law)

DC (Direct Current) voltage is constant direction: batteries (1.5V, 12V). AC (Alternating Current) voltage reverses: wall power (120V, 230V). RMS voltage = effective DC equivalent.

• DC: constant voltage (batteries, USB, circuits)
• AC: alternating voltage (wall power, grid)
• RMS = effective voltage (120V AC RMS ≈ 170V peak)
• Most devices use DC internally (AC adapters convert)

Volt (V) is the SI unit for electric potential. Defined from watt and ampere: 1 V = 1 W/A. Also: 1 V = 1 J/C (energy per charge). Prefixes from atto to giga cover all ranges.

• 1 V = 1 W/A = 1 J/C (exact definitions)
• kV for power lines (110 kV, 500 kV)
• mV, µV for sensors, signals
• fV, aV for quantum measurements

W/A and J/C are equivalent to volt by definition. Show relationships: V = W/A (power per current), V = J/C (energy per charge). Useful for understanding physics.

• 1 V = 1 W/A (from P = VI)
• 1 V = 1 J/C (definition)
• All three are identical
• Different perspectives on same quantity

Abvolt (EMU) and statvolt (ESU) from old CGS system. Rare in modern use but appear in historical physics texts. 1 statV ≈ 300 V; 1 abV = 10 nV.

• 1 abvolt = 10⁻⁸ V (EMU)
• 1 statvolt ≈ 300 V (ESU)
• Obsolete; SI volt is standard
• Appear only in old textbooks

Fundamental relationship: V = I × R. Voltage equals current times resistance. Know any two, calculate the third. Foundation of all circuit analysis.

• V = I × R (voltage = current × resistance)
• I = V / R (current from voltage)
• R = V / I (resistance from measurements)
• Linear for resistors; nonlinear for diodes, etc.

In any closed loop, voltages sum to zero. Like walking in a circle: altitude changes sum to zero. Energy is conserved. Essential for circuit analysis.

• ΣV = 0 around any loop
• Voltage rises = voltage drops
• Energy conservation in circuits
• Used to solve complex circuits

Electric field E = V/d (voltage per distance). Higher voltage over short distance = stronger field. Lightning: millions of volts over meters = MV/m field.

• E = V / d (field from voltage)
• High voltage + short distance = strong field
• Breakdown: air ionizes at ~3 MV/m
• Static shocks: kV across mm

USB: 5V (USB-A), 9V, 20V (USB-C PD). Batteries: 1.5V (AA/AAA), 3.7V (Li-ion), 12V (car). Logic: 3.3V, 5V. Laptop chargers: 19V typical.

• USB: 5V (2.5W) to 20V (100W PD)
• Phone battery: 3.7-4.2V Li-ion
• Laptop: 19V DC typical
• Logic levels: 0V (low), 3.3V/5V (high)

Home: 120V (US), 230V (EU) AC. Transmission: 110-765 kV (high voltage = low loss). Substations step down to distribution voltage. Lower voltage near homes for safety.

• Transmission: 110-765 kV (long distance)
• Distribution: 11-33 kV (neighborhood)
• Home: 120V/230V AC (outlets)
• High voltage = efficient transmission

Particle accelerators: MV to GV (LHC: 6.5 TeV). X-rays: 50-150 kV. Electron microscopes: 100-300 kV. Lightning: 100 MV typical. Van de Graaff: ~1 MV.

• Lightning: ~100 MV (100 million volts)
• Particle accelerators: GV range
• X-ray tubes: 50-150 kV
• Electron microscopes: 100-300 kV

Each prefix step = ×1000 or ÷1000. kV → V: ×1000. V → mV: ×1000. mV → µV: ×1000.

• kV → V: multiply by 1,000
• V → mV: multiply by 1,000
• mV → µV: multiply by 1,000
• Reverse: divide by 1,000

P = V × I (power = voltage × current). 12V at 2A = 24W. 120V at 10A = 1200W.

• P = V × I (Watts = Volts × Amps)
• 12V × 5A = 60W
• P = V² / R (if resistance known)
• I = P / V (current from power)

V = I × R. Know any two, find third. 12V across 4Ω = 3A. 5V ÷ 100mA = 50Ω.

• V = I × R (Volts = Amps × Ohms)
• I = V / R (current from voltage)
• R = V / I (resistance)
• Remember: divide for I or R

USB-C delivers 20V at 5A. What's the power?

P = V × I = 20V × 5A = 100W (USB Power Delivery max)

5V supply, LED needs 2V at 20mA. What resistor?

Voltage drop = 5V - 2V = 3V. R = V/I = 3V ÷ 0.02A = 150Ω. Use 150Ω or 180Ω standard.

Why transmit at 500 kV instead of 10 kV?

Loss = I²R. Same power P = VI, so I = P/V. 500 kV has 50× less current → 2500× less loss (I² factor)!

Nerve cells maintain -70 mV resting potential. Action potential spikes to +40 mV (110 mV swing) to transmit signals at ~100 m/s. Your brain is a 20W electrochemical computer!

Typical lightning bolt: ~100 MV over ~5 km = 20 kV/m field. But current (30 kA) and duration (<1 ms) cause the damage. Energy: ~1 GJ, could power a house for a month—if we could capture it!

Electric eel can discharge 600V at 1A for defense/hunting. Has 6000+ electrocytes (biological batteries) in series. Peak power: 600W. Stuns prey instantly. Nature's taser!

USB-C PD 3.1: up to 48V × 5A = 240W. Can charge gaming laptops, monitors, even some power tools. Same connector as your phone. One cable to rule them all!

Power loss ∝ I². Higher voltage = lower current for same power. 765 kV lines lose <1% per 100 miles. At 120V, you'd lose it all in 1 mile! That's why grid uses kV.

Van de Graaff generators reach 1 MV but are safe—minuscule current. Static shock: 10-30 kV. Tasers: 50 kV. Current through heart (>100 mA) is dangerous, not voltage. Voltage alone doesn't kill.

Volta invents battery (voltaic pile). First continuous voltage source. Unit later named 'volt' in his honor.

Ohm discovers V = I × R. Ohm's law becomes foundation of circuit theory. Initially rejected, now fundamental.

Faraday discovers electromagnetic induction. Shows voltage can be induced by changing magnetic fields. Enables generators.

First international electrical congress defines volt: EMF that produces 1 ampere through 1 ohm.

Westinghouse wins contract for Niagara Falls power plant. AC wins 'War of Currents'. AC voltage can be transformed efficiently.

CGPM redefines volt in absolute terms. Based on watt and ampere. Modern SI definition established.

Josephson voltage standard. Quantum effect defines volt with 10⁻⁹ accuracy. Based on Planck constant and frequency.

SI redefinition: volt now derived from fixed Planck constant. Exact definition, no physical artifact needed.

Voltage is electrical pressure (like water pressure). Current is flow rate (like water flow). High voltage doesn't mean high current. You can have high voltage with zero current (open circuit) or high current with low voltage (short circuit through wire).

Power loss in wires ∝ I² (current squared). For same power P = VI, higher voltage means lower current. 765 kV has 6,375× less current than 120V for same power → ~40 million times less loss! That's why power lines use kV.

No, current through your body kills, not voltage. Static shocks are 10-30 kV but safe (<1 mA). Tasers: 50 kV but safe. However, high voltage can force current through resistance (V = IR), so high voltage often means high current. It's the >50 mA through heart that's lethal.

DC (Direct Current) voltage is constant direction: batteries, USB, solar panels. AC (Alternating Current) voltage reverses direction: wall outlets (50/60 Hz). RMS voltage (120V, 230V) is effective DC equivalent. Most devices use DC internally (AC adapters convert).

Historical reasons. US chose 110V in 1880s (safer, less insulation needed). Europe standardized on 220-240V later (more efficient, less copper). Both work fine. Higher voltage = lower current for same power = thinner wires. Trade-off between safety and efficiency.

Yes, in series: batteries in series add voltages (1.5V + 1.5V = 3V). Parallel: voltage stays same (1.5V + 1.5V = 1.5V, but double capacity). Kirchhoff's Voltage Law: voltages in any loop sum to zero (rises equal drops).