You have a stockroom containing a large number of identical aluminum electrolytic…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
You have a stockroom containing a large number of identical aluminum electrolytic capacitors, each rated at 16V maximum and having a capacitance of 3300μF. To create a portable energy storage module, the capacitors will be connected in parallel to a 12V battery when the module is charged.
The engineering goal is to design the smallest‐possible module (fewest capacitors) that will:
• Store at least 2.0C of total charge at 12V, and
• Hold at least 12J of energy under the same conditions.
(1) Determine the minimum number of capacitors required to satisfy the charge storage criterion. Show how you arrive at your answer.
(2) Verify that this same number of capacitors also satisfies the energy storage requirement. If it does not, recalculate to find the true minimum number that meets both criteria.
(3) For the capacitor count identified in part (b), calculate (i) the equivalent capacitance, (ii) the total charge stored, and (iii) the total energy stored when connected to the 12V battery.
(4) After several months of use, one capacitor in the module becomes internally shorted and effectively removes its capacitance from the total while leaving the remaining capacitors unharmed. Recalculate the total charge and energy that the degraded module can store at 12V. Evaluate whether the module still meets either of the original design targets, and explain your reasoning thoroughly.