Poll 22: Batteries, Energy, Power, and Resistance (Video notes)

Vocabulary flashcards covering batteries in series/parallel, energy and power concepts, and practical calculations from the lecture notes.

Batteries in Series

Batteries connected end-to-end so their voltages add; ΔVtotal equals the sum of individual voltages (e.g., 3 × 1.5 V = 4.5 V).

Batteries in Series (reverse polarity)

If one battery is reversed in a series string, ΔVtotal is the algebraic sum with signs (e.g., two 1.5 V batteries forward and one reversed yield 1.5 V).

Batteries in Parallel

Batteries connected with common terminals; ΔVtotal equals the voltage of a single battery, while the current capacity increases.

Charge escalator model

A teaching model for summing voltages from multiple batteries; voltages add in series with the same orientation and subtract when one is reverse-polarity.

Potential difference (ΔV)

The voltage difference between two points; the energy per unit charge provided by a battery. ΔU = qV describes the energy change for a charge q moving through a potential difference V.

ΔU = qV

The potential energy change of a charge moving through a potential difference V: ΔU = qV.

Power (P)

The rate of energy transfer; evaluated as P = VI (also P = I^2R or P = V^2/R depending on known quantities).

Pbat = PR

In a simple single-resistor circuit, the power delivered by the battery equals the power dissipated by the resistor.

Power relationships (P = VI, P = I^2R, P = V^2/R)

Different algebraic forms of power depending on which quantities are known: P = V×I, or P = I^2×R, or P = V^2/R.

Ohm’s Law

V = IR; describes how voltage, current, and resistance relate in a circuit.

Current in a 60 W bulb at 120 V

I = P/V = 60 W / 120 V = 0.5 A.

Resistance of a 60 W bulb at 120 V

R = V^2 / P = (120 V)^2 / 60 W = 240 Ω.

Parallel bulb brightness (two identical bulbs in parallel)

Each bulb experiences the same supply voltage; brightness of each bulb is the same as the single bulb’s brightness (total brightness increases due to more current).

Power at higher voltage with same resistance

For a fixed resistance, increasing voltage increases power; specifically P ∝ V^2 (doubling V quadruples P).

Resistance comparison at the same voltage (60 W vs 100 W bulbs)

At the same voltage, the higher-wattage bulb has lower resistance (R = V^2 / P); the 60 W bulb has a larger R than the 100 W bulb.

Current in a 60 W headlamp at 12 V

I = P/V = 60 W / 12 V = 5 A.

Filament diameter from R = ρL/A

Diameter can be found from cross-sectional area A = ρL/R and A = π(d^2)/4; for the given 60 W bulb, d ≈ 0.039 mm (about 3.9×10^-5 m).

Cold vs operating resistivity in tungsten filaments

Cold resistivity is much lower than operating resistivity; this makes the initial (inrush) current much larger—approximately 10× the normal running current for the same bulb (e.g., ~5 A when hot current is 0.5 A at 120 V).