Three capacitors are connected to a battery as shown in Figure P 26.22 . Their capacitances are

step 1 Here, capacitance 2 and 3 are in parallel, so the equivalent capacitance will be 1 over 3C plus

Three capacitors are connected to a battery as shown in...

Three capacitors are connected to a battery as shown in Figure $\mathrm{P} 26.22$ . Their capacitances are $C_{1}=3 C, C_{2}=C$ , and $C_{3}=5 C .$ (a) What is the equivalent capacitance of this set of capacitors? (b) State the ranking of the capacitors according to the charge they store, from largest to smallest. (c) Rank the capacitors according to the potential differences across them, from largest to smallest. (d) What If? If $C_{3}$ is increased, what happens to the charge stored by each of the capacitors?

Key Concepts

Equivalent Capacitance

This concept involves combining multiple capacitors into a single capacitor that can replace the network, taking into account whether they are connected in series, parallel, or a combination of both. The rules differ depending on the configuration: for capacitors in series, the reciprocals of capacitances add, whereas for parallel arrangements, the capacitances add directly.

Charge-Voltage Relationship (Q = CV)

This fundamental relationship states that the charge stored on a capacitor is directly proportional to both its capacitance and the voltage across it. This equation is critical for understanding how variations in capacitance or potential difference affect the amount of charge stored in a capacitor.

Capacitors in Series and Parallel Networks

In series configurations, all capacitors hold the same charge while the voltage is divided among them according to their capacitances. In parallel configurations, each capacitor experiences the same voltage, but the charge stored is different and scales with the individual capacitance values. This distinction is essential for analyzing how charge distribution and voltage drops occur across a mixed circuit.

Impact of Changing Capacitance in a Network

Altering the capacitance of one element in a network can affect the overall equivalent capacitance, the charge distribution, and the voltage drops across each capacitor. Understanding how an increase or decrease in a single capacitor’s value influences the circuit helps in predicting the behavior of all components under changing conditions.

Please give Ace some feedback