In Fig. 25-29, a potential difference V=100 V is applied across a capacitor arrangement with ca

step 1 For this problem, we're given a circuit with three capacitors and a potential difference of 100

In Fig. 25-29, a potential difference V=100 V is applied...

In Fig. $25-29$, a potential difference $V=100 \mathrm{~V}$ is applied across a capacitor arrangement with capacitances $C_{1}=10.0 \mu \mathrm{F}$, $C_{2}=5.00 \mu \mathrm{F}$, and $C_{3}=15.0 \mu \mathrm{F}$. What are (a) charge $q_{3}$, (b) potential difference $V_{3}$, and $(\mathrm{c})$ stored energy $U_{3}$ for capacitor $3,(\mathrm{~d}) q_{1}$, (e) $V_{1}$, and (f) $U_{1}$ for capacitor 1 , and $(\mathrm{g}) q_{2}$, (h) $\dot{V}_{2}$, and (i) $U_{2}$ for capacitor $2 ?$

In Fig. $25-29$, a potential difference $V=100 \mathrm{~V}$ is applied across a capacitor arrangement with capacitances $C_{1}=10.0 \mu \mathrm{F}$, $C_{2}=5.00 \mu \mathrm{F}$, and $C_{3}=15.0 \mu \mathrm{F}$. What are (a) charge $q_{3}$, (b) potential difference $V_{3}$, and $(\mathrm{c})$ stored energy $U_{3}$ for capacitor $3,(\mathrm{~d}) q_{1}$,
(e) $V_{1}$, and (f) $U_{1}$ for capacitor 1 , and $(\mathrm{g}) q_{2}$,
(h) $\dot{V}_{2}$, and
(i) $U_{2}$ for capacitor $2 ?$

Key Concepts

Capacitance

Capacitance is a measure of a capacitor's ability to store charge per unit voltage. It is defined by the ratio q/V, where q is the charge stored, and V is the potential difference across the capacitor. The unit of capacitance is the farad (F), and it determines how much energy can be stored in the capacitor for a given voltage.

Potential Difference (Voltage)

The potential difference, or voltage, across a capacitor is the work required per unit charge to move the charge between its plates. It plays a key role in determining both the charge stored on the capacitor (via the relation q=CV) and the energy stored (using U=½CV²).

Charge Distribution in Capacitor Networks

In a network of capacitors, the distribution of charge depends on whether the capacitors are connected in series or parallel. In series, the charge on each capacitor is identical even though the voltage may vary. This relationship is used to calculate the individual charges when a total potential difference is applied to the network.

Stored Energy in a Capacitor

The energy stored in a capacitor is given by the expression U=½CV². This formula shows that the energy increases with both higher capacitance and higher voltage. Understanding this concept is fundamental when analyzing circuits to determine how much energy is stored or can be discharged from individual capacitors or networks.

Capacitors in Series and Parallel

Capacitor networks can be arranged in series, parallel, or a combination of both, which affects their equivalent capacitance. In series arrangements, capacitors share the same charge, whereas in parallel arrangements, they share the same voltage. The method of combining these arrangements is crucial for analyzing how the overall potential difference is distributed and how charge is stored within the circuit.

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