The five identical bulbs in FIGURE EX28.11 are all glowing. The battery is ideal. What is the order of brightness of the bulbs, from brightest to dimmest? Some may be equal.

검증된 단계별 안내

Analyze the circuit diagram in FIGURE EX28.11 to identify how the bulbs are connected (series, parallel, or a combination). This will help determine the current and voltage distribution across each bulb.

Recall that the brightness of a bulb is proportional to the power it dissipates, which can be expressed as \( P = I^2 R \) or \( P = \frac{V^2}{R} \), where \( I \) is the current through the bulb, \( V \) is the voltage across it, and \( R \) is the resistance of the bulb.

Determine the equivalent resistance of the circuit by simplifying the series and parallel combinations of the bulbs. This will allow you to calculate the total current supplied by the battery.

Using the total current and the rules for current and voltage distribution in series and parallel circuits, calculate the current through and voltage across each bulb. This will help you compare their power outputs.

Rank the bulbs in order of brightness based on their power outputs, noting that bulbs with the same current and voltage will have equal brightness.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Series and Parallel Circuits

In electrical circuits, components can be arranged in series or parallel configurations. In a series circuit, the same current flows through all components, leading to equal brightness if the components are identical. In a parallel circuit, each component receives the full voltage of the battery, which can result in brighter bulbs since they operate independently.

Ohm's Law

Ohm's Law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship helps determine how voltage and resistance affect the brightness of bulbs, as brightness is related to the power (P = IV) consumed by each bulb.

Power Dissipation in Resistors

The power dissipated by a resistor (or bulb) in an electrical circuit is given by the formula P = I^2R, where I is the current through the resistor and R is its resistance. For identical bulbs, the brightness is proportional to the power they dissipate; thus, understanding how current divides in series and parallel circuits is crucial for determining which bulbs will be brighter or dimmer.