OPOpenPithMake curiosity visiblePhysics lab / Middle-school electricity

About this bench

Six experiments, one thread: how current, voltage and resistance decide what a circuit does.

The first three build the basic laws: how current divides in series and parallel, how current relates to voltage and resistance, and what decides a conductor’s resistance. The last three look at what current does: it heats a conductor, and when it heats too much a fuse has to cut the circuit; it also makes a magnetic field, and a coil with an iron core becomes an electromagnet.

Every reading, needle and curve comes from the same circuit model, not a pre-drawn animation. The dots in the wires move at a speed set by the current. Change one parameter and all the data is recalculated together.

What each experiment shows

Six sets of data, six intuitions overturned.

  • Series and parallel: in series all three ammeters agree, so bulbs do not use up current. In parallel the main current is the sum of the two branches. Unscrew one bulb: in series everything goes out; in parallel the other bulb stays lit.
  • Ohm’s law: for one resistor the U-I graph is a straight line through the origin. Double the voltage and the current doubles; U/I stays the same. Resistance is a property of the conductor, not set by the voltage.
  • What sets resistance: double the length and the resistance doubles; double the diameter and the cross-section is 4 times larger, so the resistance falls to 1/4; a manganin wire of the same size has only 0.4 times the resistance of nichrome.
  • Joule’s law: with 5 Ω and 10 Ω in series, flask B always rises twice as much as flask A. Double the current and the rise becomes 4 times larger. In series, the bigger resistance gives more heat.
  • Short circuits and fuses: in a short circuit the current can exceed 30 times its normal value while the bulbs go dark; the fuse melts within milliseconds. Replace the fuse with copper wire and the circuit loses its protection.
  • Electromagnet: more current and more turns lift more pins. Pull out the nail and the same coil lifts almost none.

Model and sources

Model and sources

  • Series and parallel: two dry cells, E = 3.0 V, internal resistance 0.8 Ω. A bulb’s resistance rises with voltage, R = Rc + β√U; at switch-on it starts from the cold resistance and reaches its steady value with a 0.06 s time constant.
  • Ohm’s law: a 3 V supply and ideal meters; current is read to 0.01 A and voltage to 0.01 V.
  • What sets resistance: R = ρL/S. Nichrome 1.1 Ω·mm²/m, manganin 0.44 Ω·mm²/m; one dry cell, 1.5 V, internal resistance 0.5 Ω.
  • Joule’s law: 0.10 kg of kerosene per flask, specific heat 2.1×10³ J/(kg·℃); mc·dT/dt = I²R − k(T − T₀), heat-loss coefficient k = 0.02 W/℃.
  • Short circuits and fuses: a 6 V supply with 0.3 Ω internal resistance; “6 V 3 W” bulbs taken as 12 Ω; the fuse is 0.05 Ω, melts at twice its rated current, heats with a 0.5 s time constant and melts at 250 ℃.
  • Electromagnet: at the pole B ≈ μ₀μr·N·I / (2ℓ), ℓ = 5 cm, nail μr = 60; one pin is lifted for every 6 mT of B, up to 30 pins.

These values are teaching assumptions for comparison, not measurements: the internal resistance of the cells and supply, the cold filament resistance and its time constant, the meter-needle damping, the kerosene heat-loss coefficient, the fuse’s fusing ratio and time constant, the nail’s effective permeability, and the pins-per-millitesla rule. The resistivities of nichrome and manganin and the specific heat of kerosene are textbook values. OpenStax gives 1.0 Ω·mm²/m for nichrome, about 9 % below the textbook value; alloys of different composition differ by this much.

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