Question

consider a circuit containing five identical light bulbs and an ideal battery. assume that the resistance of each light bulb remains constant. rank the bulbs (a through e) based on their brightness. rank from brightest to dimmest. to rank items as equivalent, overlap them. view available hint(s)

Explanation:

Step1: Recall power - brightness relation

The brightness of a light - bulb is related to the power dissipated in it, $P = I^{2}R= \frac{V^{2}}{R}$. Since the bulbs are identical (same $R$), brightness depends on current $I$ or voltage $V$ across the bulb.

Step2: Analyze series - parallel circuit properties

In a series circuit, the current through each component is the same, and in a parallel circuit, the voltage across each parallel branch is the same. The total current in the circuit is divided among parallel branches.

Step3: Analyze bulb A

Bulb A is in a position where it has the full current of one of the main branches flowing through it.

Step4: Analyze bulb B

Bulb B is in a parallel combination with other bulbs in its sub - branch. The current through it is less than the current through A because the current in the main branch is divided among the parallel bulbs in its sub - branch.

Step5: Analyze bulb C

Bulb C is also in a parallel sub - branch. The current through it is less than A. Also, depending on the circuit configuration, its current may be different from B.

Step6: Analyze bulb D

Bulb D is in a parallel sub - branch. Its current is less than A.

Step7: Analyze bulb E

Bulb E is in a parallel sub - branch. Its current is less than A.

Step8: Compare currents and rank

The bulb with the most current through it will be the brightest. Assuming a well - formed circuit with proper parallel and series combinations, if bulb A has the most current flowing through it, followed by B, C, D, and E in decreasing order of current.

Answer:

A > B > C > D > E