Two Lamps, One Battery: Series vs. Parallel
A student builds a circuit with a 6 V battery and two identical lamps, each with resistance 12 Ω. In arrangement A the lamps are wired in series; in arrangement B they are wired in parallel. In arrangement A both lamps glow dimly. In arrangement B both glow brightly, but after a few minutes the battery feels warm and the student notices the wires are warmer too. The student says: 'Parallel is better because the lamps are brighter, so I should always use parallel.' The teacher asks the student to compare the total current and power in each arrangement and to explain the trade-off.
1. Calculate the total resistance, total current, and total power for arrangement A (series) and arrangement B (parallel).
Read the worked answer
Series (A): R_total = 12 + 12 = 24 Ω. I = V/R = 6/24 = 0.25 A. P = V·I = 6 × 0.25 = 1.5 W total (0.75 W per lamp).
Parallel (B): Each branch sees the full 6 V. Branch current = 6/12 = 0.5 A each, so total I = 1.0 A. R_total = 6/1.0 = 6 Ω. P = 6 × 1.0 = 6 W total (3 W per lamp).
So parallel draws 4× the current and delivers 4× the power compared with series. That is why the lamps are brighter - and why the battery and wires warm up more.
2. Explain the trade-off the student missed, and give one situation where series wiring would be the better choice.
Read the worked answer
Brighter is not automatically 'better.' Higher current in parallel means more power drawn from the battery, faster battery drain, and more heating in the wires (P = I²R in the wires), which can be a safety concern. The parallel arrangement also means that if one lamp fails open, the other keeps working - an advantage for reliability.
Series is better when you want to limit current or share voltage: e.g., old-style decorative light strings where many small bulbs share a high voltage, or a circuit where you need to protect a component from too much current. The cost is that a single broken lamp opens the whole series circuit, and each lamp gets less voltage (3 V each here instead of 6 V).