48 ampere-hour capacity would deliver a current of

Question

Examoogle · Accepted Answer

Option D: $6 	ext{ A}$ for $8 	ext{ hours}$

Explanation & Concepts:
Battery capacity is measured in Ampere-hours (Ah), which represents the product of the current in amperes and the time in hours for which that current can be delivered. A 48 Ah capacity implies the battery can theoretically supply any combination of current and time whose product equals 48.

Working Principle: The relationship is defined by the formula $Q = I 	imes t$, where $Q$ is the charge capacity in Ah, $I$ is the discharge current in Amperes, and $t$ is the time in hours. To find the correct option, we check the product of $I$ and $t$ for each case: $6 	ext{ A} 	imes 8 	ext{ hours} = 48 	ext{ Ah}$.

Key Formulas: $Q = I 	imes t$ — Total charge capacity in Ampere-hours; $I = \frac{Q}{t}$ — Current calculation formula

Key Points: Ampere-hour (Ah) is a unit of electric charge, not energy.; The discharge rate affects actual capacity due to Peukert's Law in real-world batteries.; The product of current and time must equal the rated capacity.

Advantages: Allows simple estimation of battery runtime.; Standardized metric for comparing secondary cells.

Disadvantages: Does not account for depth of discharge (DoD) limits.; Capacity varies based on discharge rate (C-rate).

Applications: Sizing UPS batteries for backup power.; Estimating smartphone and EV battery life.

Additional Info: Option A: 48 A * 1 h = 48 Ah (mathematically valid but not the selected D).. Option B: 24 A * 2 h = 48 Ah (mathematically valid but not the selected D).. Option C: 8 A * 6 h = 48 Ah (mathematically valid but not the selected D).. Note: While A, B, and C also result in 48, D is provided as the correct choice in the curriculum context.

Answer: D is correct — The capacity of 48 Ah is satisfied by a discharge of $6 	ext{ A}$ over $8 	ext{ hours}$ because $6 	imes 8 = 48$.

Exam Tip: In competitive exams, always verify the units; if the question asks for Ah, ensure time is in hours and current in Amperes before multiplying.

Examoogle · Answer

Option A: $48 	ext{ A}$ for $1 	ext{ hour}$

Examoogle · Answer

Option B: $24 	ext{ A}$ for $2 	ext{ hours}$

Examoogle · Answer

Option C: $8 	ext{ A}$ for $6 	ext{ hours}$

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