Two capacitors C1=5.00 μF and C2=12.0 μF are connected in...

Two capacitors $C_{1}=5.00 \mu \mathrm{F}$ and $C_{2}=12.0 \mu \mathrm{F}$ are connected in parallel, and the resulting combination is connected to a $9.00-\mathrm{V}$ battery. (a) What is the value of the equivalent capacitance of the combination? What are (b) the potential difference across each capacitor and (c) the charge stored on each capacitor?

Two capacitors $C_{1}=5.00 \mu \mathrm{F}$ and $C_{2}=12.0 \mu \mathrm{F}$ are connected in parallel, and the resulting combination is connected to a $9.00-\mathrm{V}$ battery. (a) What is the value of the equivalent capacitance of the combination? What are
(b) the potential difference across each capacitor and
(c) the charge stored on each capacitor?

Key Concepts

Capacitors in Parallel

When capacitors are connected in parallel, they are arranged so that their corresponding terminals are connected to the same nodes in the circuit. This configuration results in each capacitor experiencing the same voltage across its plates. The individual capacitances simply add up to give the total capacitance of the network.

Equivalent Capacitance

The equivalent capacitance of a configuration of capacitors represents the single capacitance that would store the same amount of charge at a given voltage as the entire network. In a parallel arrangement, the equivalent capacitance is the sum of the individual capacitances, making it straightforward to compute.

Potential Difference in Parallel Circuits

In a parallel circuit, all components are connected across the same two nodes, which means that the potential difference (voltage) across each capacitor is the same as the voltage of the power source. This uniformity in voltage simplifies the analysis of the circuit and ensures that each capacitor is charged to the same potential difference.

Charge Storage in Capacitors (Q = CV)

Capacitors store energy in the form of an electric field between their plates, and the amount of charge stored on a capacitor is directly proportional to the capacitance and the voltage across it. This relationship is expressed by the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. Understanding this relationship is key for analyzing circuits involving capacitors.

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