In Fig. E24.20, C1= 6.00 μF, C2=3.00 μF, and C3= 5.00 μF. The capacitor networ

step 1 Hi everyone here it is given. Capistar C1 is 6 microferret C2 is 3 microferret C3 is 5 microferr

In Fig. E24.20, C1= 6.00 μF, C2=3.00 μF,...

$\begin{array}{llll}& \text { In } & \text { Fig. } & \text { E24.20, } & C_{1}=\end{array}$ $6.00 \mu \mathrm{F}, C_{2}=3.00 \mu \mathrm{F},$ and $C_{3}=$ $5.00 \mu \mathrm{F}$. The capacitor network is connected to an applied potential $V_{a b}$. After the charges on the capacitors have reached their final values, the charge on $C_{2}$ is $30.0 \mu \mathrm{C}$. (a) What are the charges on capacitors $C_{1}$ and $C_{3} ?$ (b) What is the applied voltage $V_{a b} ?$

$\begin{array}{llll}& \text { In } & \text { Fig. } & \text { E24.20, } & C_{1}=\end{array}$
$6.00 \mu \mathrm{F}, C_{2}=3.00 \mu \mathrm{F},$ and $C_{3}=$
$5.00 \mu \mathrm{F}$. The capacitor network is connected to an applied potential $V_{a b}$. After the charges on the capacitors have reached their final values, the charge on $C_{2}$ is $30.0 \mu \mathrm{C}$. (a) What are the charges on capacitors $C_{1}$ and $C_{3} ?$
(b) What is the applied voltage $V_{a b} ?$

Key Concepts

Equivalent Capacitance Calculation

To simplify the analysis of complex capacitor networks, portions of the circuit can often be replaced by an equivalent capacitor that has the same effect on the overall circuit. For series combinations, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances, whereas for parallel combinations the equivalent capacitance is the sum of the capacitances. This technique is essential for determining the overall charge distribution and the relative voltage drops across each capacitor when an external voltage is applied.

Series and Parallel Combinations in Capacitor Networks

In capacitor networks, capacitors can be connected in series or in parallel, each configuration having its own rules for charge and voltage distribution. In series arrangements, all capacitors have the same charge while the voltage across each may vary, and the equivalent capacitance is reduced compared to individual capacitances. In parallel arrangements, every capacitor experiences the same voltage, but the charges stored on the capacitors may differ proportionally to their capacitances, and the equivalent capacitance is the sum of all individual capacitances.

Capacitance, Charge, and Voltage Relationship

Capacitors store electrical energy such that the charge stored (Q) is directly proportional to both the capacitance (C) and the voltage (V) applied across it, which is described by the equation Q = CV. This fundamental relationship is used to analyze how capacitors behave in a circuit when subject to an applied voltage and is the basis for understanding charge distribution and voltage drops in capacitor networks.

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