Two parallel-plate capacitors, 6.0μF each, are connected in parallel to a 10 V battery. One of t

step 1 All right. So for this problem, we are given a circuit with two capacities connecting in paralle

Two parallel-plate capacitors, 6.0μF each, are connected in...

Two parallel-plate capacitors, 6.0$\mu \mathrm{F}$ each, are connected in parallel to a 10 $\mathrm{V}$ battery. One of the capacitors is then squeezed so that its plate separation is 50.0$\%$ of its initial value. Because of the squeczing, (a) how much additional charge is transferred to the capacitors by the battery and (b) what is the increase in the total charge stored on the capacitors?

Two parallel-plate capacitors, 6.0$\mu \mathrm{F}$ each, are connected in
parallel to a 10 $\mathrm{V}$ battery. One of the capacitors is then squeezed so
that its plate separation is 50.0$\%$ of its initial value. Because of the squeczing, (a) how much additional charge is transferred to the capacitors by the battery and (b) what is the increase in the total
charge stored on the capacitors?

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Key Concepts

Constant Voltage Source and Charge Redistribution

In circuits powered by a constant voltage source, such as a battery, the voltage across the capacitors remains fixed even if the capacitance changes. When a capacitor’s capacitance increases (for instance, by reducing the plate separation), additional charge is drawn from the battery to maintain the constant voltage, leading to a redistribution of charge in the circuit.

Capacitance of a Parallel-Plate Capacitor

A parallel?plate capacitor’s capacitance is determined by the formula C = ??A/d, where ?? is the permittivity of free space, A is the plate area, and d is the separation between the plates. This relationship shows that decreasing the distance d between the plates increases the capacitance since the ability of the capacitor to store charge improves when the plates are closer together.

Capacitors in Parallel

When capacitors are connected in parallel, their equivalent capacitance is the sum of the individual capacitances. Each capacitor experiences the same voltage across its terminals, and the total charge stored in the system is the sum of the charges on each capacitor. This concept is crucial when analyzing circuits in which one capacitor's characteristics change, as any modification directly alters the total stored charge.

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