Two Lamps, One Battery: Predicting Brightness
A student builds two circuits using the same 6.0 V battery and two identical lamps, each with resistance 12 Ω. In Circuit A, the lamps are connected in series. In Circuit B, they are connected in parallel. The student measures total current with an ammeter and observes brightness. She predicts that the series circuit will draw more current because 'the current has to push through both lamps, so it builds up.' She also notices the battery warms noticeably in Circuit B but not in Circuit A. The battery has a small internal resistance of 0.50 Ω.
1. Calculate the total resistance and current for each circuit, ignoring internal resistance, and compare brightness.
Read the worked answer
Circuit A (series): R = 12 + 12 = 24 Ω. I = V/R = 6.0/24 = 0.25 A. Each lamp gets the same 0.25 A; power per lamp = I²R = 0.25² × 12 = 0.75 W.
Circuit B (parallel): 1/R = 1/12 + 1/12 = 2/12, so R = 6.0 Ω. I = 6.0/6.0 = 1.0 A total, split 0.50 A per lamp. Power per lamp = 0.50² × 12 = 3.0 W.
Parallel lamps are much brighter (3.0 W vs 0.75 W each). The student's prediction is backwards: series has higher resistance and lower current.
2. Explain why the battery warms more in Circuit B, using the internal resistance value.
Read the worked answer
The battery's internal resistance dissipates power as heat: P = I²r. In Circuit B the total current is about 1.0 A, so heat power ≈ 1.0² × 0.50 = 0.50 W. In Circuit A the current is 0.25 A, so heat power ≈ 0.25² × 0.50 = 0.031 W, about 16 times less. Larger current in the parallel circuit means more internal heating, which is why the battery warms noticeably only in Circuit B.
3. A classmate says 'current is used up as it passes through each lamp in series.' Use the series current value to refute this.
Read the worked answer
In a series circuit the current is the same at every point. The measured 0.25 A flows through the battery, the first lamp, the second lamp, and back. Charge is not consumed; what decreases is electric potential energy, which the lamps convert to light and heat. If current were used up, the second lamp would be dimmer, but identical lamps in series have equal brightness.