In a combined circuit with a series bulb and a parallel pair, how do the brightness levels compare according to the source?

In a combined circuit with a series bulb and a parallel pair, how do the brightness levels compare according to the source?

• A. Series bulb is brightest; parallel bulbs have equal brightness and are dimmer than the series bulb.
• B. Series and parallel bulbs have equal brightness.
• C. Parallel bulbs are brighter than the series bulb.
• D. The series bulb is dimmer than the parallel bulbs.

Answer: (A)

When brightness depends on power, imagine one bulb in series with a pair of identical bulbs in parallel. The current flow through the series bulb is the same as the total current entering the parallel branch, but that current then splits between the two parallel bulbs. Because they are identical, each parallel bulb gets about half of the branch current and thus has less power than the series bulb. The voltage across the parallel pair is shared with the series bulb, so the parallel branch sits at a lower voltage than the source. Each parallel bulb sees this reduced voltage, so both are dimmer, and they glow with equal brightness since they have the same resistance and the same voltage across them. In contrast, the series bulb carries the full current of the circuit and, with its own resistance, ends up dissipating more power than either parallel bulb. Therefore the series bulb is the brightest, while the two parallel bulbs have equal, lesser brightness.

When brightness depends on power, imagine one bulb in series with a pair of identical bulbs in parallel. The current flow through the series bulb is the same as the total current entering the parallel branch, but that current then splits between the two parallel bulbs. Because they are identical, each parallel bulb gets about half of the branch current and thus has less power than the series bulb. The voltage across the parallel pair is shared with the series bulb, so the parallel branch sits at a lower voltage than the source. Each parallel bulb sees this reduced voltage, so both are dimmer, and they glow with equal brightness since they have the same resistance and the same voltage across them. In contrast, the series bulb carries the full current of the circuit and, with its own resistance, ends up dissipating more power than either parallel bulb. Therefore the series bulb is the brightest, while the two parallel bulbs have equal, lesser brightness.