Real sources, measurement, and safety
Ideal sources and meters are approximations. Real batteries sag, real meters load circuits, and real electricity can injure, so engineers must understand the practical side.
Real voltage sources
A real battery or power supply behaves like an ideal voltage source in series with an internal resistance. Under load, the terminal voltage drops: \(V_{terminal} = V_{oc} - iR_{int}\). A car battery has very low internal resistance, under 0.01 \(\Omega\), so it can deliver hundreds of amperes to a starter motor; a coin cell has much higher internal resistance and can supply only small currents.
Batteries
Batteries store chemical energy. Capacity is quoted in ampere-hours (Ah) or milliampere-hours; energy is capacity times voltage, in watt-hours. Common chemistries include alkaline (1.5 V per cell, non-rechargeable), nickel-metal hydride (1.2 V), and lithium-ion (about 3.6 to 3.7 V nominal), which powers phones, laptops, and electric cars with high energy density but requires careful charging and protection.
Connecting cells
Cells in series add voltages while capacity stays the same: four 1.5 V alkaline cells give 6 V. Cells in parallel add capacity at the same voltage. Battery packs in electric vehicles combine many lithium-ion cells in series and parallel, with battery management systems balancing cells and preventing overcharge, over-discharge, and overheating.
Measurement errors
A voltmeter with finite resistance draws current, slightly lowering the voltage it measures, especially in high-resistance circuits; digital multimeters typically have around 10 M\(\Omega\) input resistance. An ammeter adds a small resistance in series, called burden. Choosing meters whose resistance is far larger (voltmeters) or far smaller (ammeters) than the circuit's keeps errors small.
Electrical safety
Current through the body, not voltage alone, causes harm. Around 1 mA can be felt; about 10 to 20 mA can cause muscles to lock so a victim cannot let go; and currents around 100 mA through the chest can cause ventricular fibrillation, which is often fatal. Dry skin offers considerable resistance, but wet skin or broken skin lowers it dramatically, which is why mains voltages and water are so dangerous.
Protective devices
Fuses melt and circuit breakers trip when current exceeds a rating, protecting wiring from overheating and fire. Residual-current devices (RCDs), called ground-fault circuit interrupters (GFCIs) in North America, compare current in the live and neutral conductors and disconnect within tens of milliseconds if a few milliamperes leak, for example through a person, typically at 30 mA or less. Earthing (grounding) metal cases gives fault current a safe path.
Safe working practice
Before working on equipment, switch off and isolate it, lock or tag the isolation, and verify the absence of voltage with a tested meter. Treat capacitors as possibly charged. Use insulated tools and appropriate meter categories (CAT ratings) for the circuit. Many jurisdictions require qualified electricians for mains wiring. Low-voltage electronics projects avoid most of these hazards.
Worked example
A battery shows 12.6 V with no load. Connected to a starter motor drawing 150 A, its terminal voltage falls to 11.1 V. The internal resistance is \(R_{int} = \frac{12.6 - 11.1}{150} = 0.01\) \(\Omega\). The power lost inside the battery is \(150^2 \times 0.01 = 225\) W, which is why batteries warm up under heavy loads.
Key takeaways
Real sources have internal resistance, so terminal voltage drops under load: V = V_oc - i R_int. Batteries store chemical energy, with capacity in ampere-hours and energy in watt-hours; alkaline, NiMH, and lithium-ion cells have different voltages and uses. Series cells add voltage; parallel cells add capacity; packs need battery management. Meters load circuits; voltmeters need high resistance and ammeters low. Body current causes harm: about 1 mA is felt, 10 to 20 mA prevents letting go, and about 100 mA can cause fibrillation. Fuses, breakers, RCDs or GFCIs, and earthing protect people and wiring. Isolate, lock, test, and respect mains voltage.
Flashcard
Resistance inside a real source
Check your understanding
Why does an RCD (GFCI) protect people better than an ordinary fuse?