Two air-filled, parallel-plate capacitors are to be connected to a 10 V battery, first individua

step 1 All right, so in this problem, we already know that we have two capacitors, C1, C2, and we did f

Two air-filled, parallel-plate capacitors are to be...

Two air-filled, parallel-plate capacitors are to be connected to a 10 $\mathrm{V}$ battery, first individually, then in series, and then in parallel. In those arrangements, the energy stored in the capacitors turns out to be, listed least to greatest: $75 \mu \mathrm{J}, 100 \mu \mathrm{J}, 300 \mu \mathrm{J},$ and 400$\mu \mathrm{J}$ Of the two capacitors, what is the (a) smaller and (b) greater capacitance?

Two air-filled, parallel-plate capacitors are to be connected to a
10 $\mathrm{V}$ battery, first individually, then in series, and then in parallel. In
those arrangements, the energy stored in the capacitors turns out to be, listed least to greatest: $75 \mu \mathrm{J}, 100 \mu \mathrm{J}, 300 \mu \mathrm{J},$ and 400$\mu \mathrm{J}$ Of the
two capacitors, what is the (a) smaller and (b) greater capacitance?

Key Concepts

Equivalent Capacitance in Series and Parallel

When capacitors are connected in series, the overall or equivalent capacitance is reduced because the reciprocals add (1/C_eq = 1/C1 + 1/C2 + ...). In parallel, the capacitances add directly (C_eq = C1 + C2 + ...), increasing the total capacitance. This is crucial when determining how energy storage changes with different arrangements.

Voltage Distribution in Series Configurations

In a series configuration, the applied voltage from a battery is divided between the capacitors based on their capacitances. This division alters the voltage each capacitor experiences, which in turn affects the energy stored in each capacitor as per the energy formula. Understanding voltage distribution is key when analyzing the energy storage in series connections.

Capacitor

A capacitor is an electronic component that stores electrical energy in an electric field created between a pair of conductors. Its ability to store charge is quantified by its capacitance, which depends on geometric factors and the properties of the dielectric material between the plates.

Energy Stored in a Capacitor

The energy stored in a capacitor is given by the equation U = 1/2 C V², where U is the energy, C is the capacitance, and V is the voltage across the capacitor. This relationship shows that for a fixed voltage, the energy stored is directly proportional to the capacitance.

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