A 10.0-μF capacitor is charged to 15.0 V . It is next connected in series with an uncharged 5.00

step 1 Here, the first thing we are going to find is Q equals C, delta V, equals 10 microfarad times 15

A 10.0-μF capacitor is charged to 15.0 V . It is next...

A $10.0-\mu \mathrm{F}$ capacitor is charged to 15.0 $\mathrm{V}$ . It is next connected in series with an uncharged $5.00-\mu \mathrm{F}$ capacitor. The series combination is finally connected across a $50.0-\mathrm{V}$ battery as diagrammed in Figure $\mathrm{P} 26.54$ . Find the new potential differences across the $5.00-\mu \mathrm{F}$ and $10.0-\mu \mathrm{F}$ capacitors.

Key Concepts

Capacitor

A capacitor is an electronic component that stores electrical energy in an electric field. Its ability to store charge is determined by its capacitance, which is defined by the ratio of the charge stored on the capacitor to the voltage across it (Q = CV). Understanding capacitance is fundamental to analyzing how energy is stored and released in circuits.

Capacitors in Series

When capacitors are connected in series, they share the same charge while the total voltage across the series arrangement is the sum of the voltages across each capacitor. This property means that the individual voltages are determined by both the capacitance values and the common charge, and it is critical when analyzing how the voltage divides across each element in the series configuration.

Equivalent Capacitance

The equivalent capacitance of a series combination of capacitors is found using the reciprocal formula 1/C_eq = 1/C1 + 1/C2 + ... . This concept allows us to simplify a series network of capacitors into a single capacitor with an effective capacitance, which is essential for analyzing the overall behavior of the circuit, especially in transient analysis and in steady-state conditions when connected to a voltage source.

Charge Redistribution

In circuits where initially charged and uncharged capacitors are connected together, charge redistribution occurs until the system reaches equilibrium. In a series circuit, the requirement that the same charge must flow through all elements forces the redistribution of charge so that the final voltage drops adjust in accordance with both the initial conditions and any external influences, such as battery voltage.

Battery as a Voltage Source

A battery acts as a constant voltage source that imposes a fixed potential difference across the circuit it is connected to. When connected to a network of capacitors, the battery influences how the voltages across individual capacitors adjust so that their sum matches the battery voltage. This interaction is key to determining the final steady-state conditions in circuits containing pre-charged elements or varying capacitances.

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