Question

compare the brightness of bulbs in a series circuit versus a parallel circuit, assuming identical bulbs and the same voltage source.
bulbs in series are brighter
both are equally bright
bulbs in parallel are brighter
cannot be determined

Explanation:

Step1: Recall power formula for bulbs

The brightness of a bulb depends on its power output, given by $P = \frac{V^2}{R}$, where $V$ is the voltage across the bulb and $R$ is its resistance.

Step2: Analyze series circuit voltage

For identical bulbs in series, the total voltage $V_{source}$ is split equally between $n$ bulbs: $V_{series} = \frac{V_{source}}{n}$. The power of each bulb is $P_{series} = \frac{(V_{source}/n)^2}{R} = \frac{V_{source}^2}{n^2 R}$.

Step3: Analyze parallel circuit voltage

For identical bulbs in parallel, each bulb receives the full source voltage: $V_{parallel} = V_{source}$. The power of each bulb is $P_{parallel} = \frac{V_{source}^2}{R}$.

Step4: Compare power outputs

Since $n \geq 2$ (multiple bulbs to compare circuits), $\frac{V_{source}^2}{R} > \frac{V_{source}^2}{n^2 R}$, so $P_{parallel} > P_{series}$.

Answer:

Bulbs in parallel are brighter