(II) A 0.40-μF and a 0.60-μF capacitor are connected in series to a 9.0-V battery. Calculate (a)

step 1 When the capacitors are connected in series, then net capacitance decreases and charge on each c

(II) A 0.40-μF and a 0.60-μF capacitor are connected in...

(II) A $0.40-\mu \mathrm{F}$ and a $0.60-\mu \mathrm{F}$ capacitor are connected in series to a 9.0-V battery. Calculate (a) the potential difference across each capacitor, and (b) the charge on each. (c) Repeat parts (a) and (b) assuming the two capacitors are in parallel.

Key Concepts

Capacitor

A capacitor is an electrical component that stores energy in an electric field between two conductive plates separated by an insulating material. Its ability to store charge is characterized by its capacitance (C), which is defined by the relation Q = CV, where Q is the charge stored and V is the potential difference across the plates.

Capacitors in Series

In a series configuration of capacitors, the same charge flows through each capacitor, meaning each capacitor stores an equal amount of charge. However, the potential difference across each capacitor may differ and is determined by its capacitance, with the total voltage being the sum of the individual voltages. The equivalent capacitance for capacitors in series is found using the formula 1/C_eq = 1/C1 + 1/C2 + ... + 1/Cn.

Capacitors in Parallel

For capacitors connected in parallel, each capacitor experiences the same potential difference as the applied voltage across the combination. The charge on each capacitor, however, can be different, as it depends on its own capacitance. The equivalent capacitance is simply the sum of the individual capacitances, given by C_eq = C1 + C2 + ... + Cn.

Equivalent Capacitance

Equivalent capacitance refers to the single capacitance that can replace a network of capacitors without changing the overall behavior of the circuit. Its calculation differs based on whether the capacitors are connected in series or parallel, impacting how charge and voltage distribute across them.

Charge and Voltage Relationship in Capacitors

The fundamental relationship for a capacitor is Q = CV, which ties together the stored charge (Q), the capacitance (C), and the voltage (V) across the capacitor. This relationship is central to analyzing circuits involving capacitors, determining how much charge is stored given a certain potential difference or vice versa.

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