26. Capacitors & Dielectrics

An isolated capacitor C₁ carries a charge Q₀. Its wires are then connected to those of a second capacitor C₂, previously uncharged. What charge will each carry now? What will be the potential difference across each?

A parallel-plate capacitor has square plates 12 cm on a side separated by 0.10 mm of plastic with a dielectric constant of K = 3.8. The plates are connected to a battery, causing them to become oppositely charged. Since the oppositely charged plates attract each other, they exert a pressure on the dielectric. If this pressure is 40.0 Pa, what is the battery voltage?

A parallel-plate air capacitor of capacitance $245$ pF has a charge of magnitude $0.148$ $\mu$C on each plate. The plates are $0.328$ mm apart.

(a) What is the potential difference between the plates?

(b) What is the area of each plate?

(c) What is the electric field magnitude between the plates?

(d) What is the surface charge density on each plate?

A parallel-plate capacitor with plate area 2.0 cm² and air-gap separation 0.50 mm is connected to a 12-V battery, and fully charged. The battery is then disconnected. The plates are now pulled to a separation of 0.85 mm. What is the charge on the capacitor now?

Two 2.0 cm×2.0 cm metal electrodes are spaced 1.0 mm apart and connected by wires to the terminals of a 9.0 V battery. The wires are disconnected, and insulated handles are used to pull the plates apart to a new spacing of 2.0 mm. What are the charge on each electrode and the potential difference between them?

Small distances can be measured using a capacitor whose plate separation 𝓍 is variable. Consider an air-filled parallel-plate capacitor with fixed plate area A = 25 mm² separated by a variable distance 𝓍. Assume this capacitor is attached to a capacitance-measuring instrument which can measure capacitance C in the range 1.0 pF to 1000.0 pF with an accuracy of ∆C = 0.1 pF. Determine the percent accuracy to which 𝓍_min and 𝓍_max can be measured.

Small distances can be measured using a capacitor whose plate separation 𝓍 is variable. Consider an air-filled parallel-plate capacitor with fixed plate area A = 25 mm² separated by a variable distance 𝓍. Assume this capacitor is attached to a capacitance-measuring instrument which can measure capacitance C in the range 1.0 pF to 1000.0 pF with an accuracy of ∆C = 0.1 pF. If C is measured while 𝓍 is varied, over what range ( 𝓍_min ≤ 𝓍 ≤ 𝓍_max) can the plate-separation distance (in μm) be determined by this setup?