OPOpenPithMake curiosity visiblePhysics lab / High-school electricity

About this lab

Six experiments, one thread: where the energy in a circuit comes from, where it is stored, and how it moves.

The first two deal with measuring DC circuits: a source has internal resistance, so its terminal voltage falls as the current rises; a filament heats up, so its resistance is not fixed, and the measuring method itself brings errors. The last four deal with circuits that change: a capacitor stores energy in an electric field and a coil stores it in a magnetic field; join them and the energy swings back and forth as an oscillation. A transformer passes energy through a changing flux, so it only works with AC.

Every reading, oscilloscope trace and fit comes from the same circuit model, not a pre-drawn animation. Capacitor voltage and coil current never jump. Change one parameter and all the data is recalculated together.

What each experiment shows

Six sets of data, six intuitions overturned.

  • EMF and internal resistance: the smaller the external resistance, the larger the current and the lower the terminal voltage. The U-I intercept is the EMF and the slope’s magnitude is the internal resistance. With the voltmeter across the cell plus ammeter, the measured r includes the ammeter’s extra 0.5 Ω.
  • I-V curve: a small bulb’s I-U graph bends toward the voltage axis. From low to high voltage the filament resistance rises from about 4 Ω to about 12 Ω. The limiting connection cannot reach 0 V, so the curve is plotted with the divider connection.
  • Capacitor: the voltage rises exponentially and reaches 63 % of the supply voltage after one time constant τ = RC. On discharge the current reverses, and after one τ 37 % is left.
  • Self-induction: the bulb flashes at switch-off only when the coil resistance is below the bulb’s, so the coil current is larger than the bulb current. The bulb current reverses, and the energy released equals the ½LI² stored in the coil.
  • Oscillation: capacitor voltage and coil current are a quarter period apart, and energy moves back and forth between the electric and magnetic fields. The period T = 2π√(LC) does not depend on the charging voltage; a larger coil resistance makes the oscillation die out faster.
  • Transformer: with AC, U₂ / U₁ = n₂ / n₁ and input power equals output power; stepping up the voltage steps down the current. With DC the secondary has a voltage only at the moment of switch-on, then 0.

Model and sources

Model and sources

  • EMF: one dry cell, E = 1.5 V, internal resistance 0.5, 1 or 2 Ω; voltmeter 3 kΩ, ammeter 0.5 Ω; readings to 0.01 V and 0.01 A, fitted to U = E − Ir by least squares.
  • I-V curve: a “3.8 V 0.3 A” bulb, R = Rc + β√U; 4.0 V supply, 10 Ω rheostat; ideal meters.
  • Capacitor: 6 V supply, u = E(1 − e^(−t/RC)), discharge u = U₀e^(−t/RC); one sample every τ/50, and the measured τ is the first sample at or above 63.2 %.
  • Self-induction: 3 V supply, bulb taken as a fixed 10 Ω, coil L = 1 H; closed, i = (E/R_L)(1 − e^(−tR_L/L)); opened, i = I₀e^(−t(R_L + R_A)/L).
  • Oscillation: u_C = U₀e^(−αt)(cos ω_d t + (α/ω_d) sin ω_d t), α = R/2L, ω₀ = 1/√(LC); the oscilloscope samples at 20 kHz and the period is measured between zero crossings.
  • Transformer: ideal, U₂ = U₁n₂/n₁, P₁ = P₂; the secondary drives a “12 V 6 W” bulb taken as 24 Ω; for DC the primary has L₁ = 0.1 H and R₁ = 2 Ω.

These values are teaching assumptions for comparison, not measurements: the cell and meter resistances, the cold filament resistance, the meter-needle damping, the inductance and resistance of the self-induction coil, the inductance, capacitance and coil resistance of the LC circuit, and the primary inductance and resistance of the transformer. The ideal transformer ignores flux leakage and core losses; a real demountable transformer gives a slightly smaller U₂ than n₂/n₁ predicts.

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