Chapter 24: Problem 46
The capacitor in an automatic external defibrillator is charged to \(7.50 \mathrm{kV}\) and stores \(2400 .\) J of energy. What is its capacitance?
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A \(4.00 \cdot 10^{3}\) -nF parallel plate capacitor is connected to a 12.0 -V battery and charged. a) What is the charge \(Q\) on the positive plate of the capacitor? b) What is the electric potential energy stored in the capacitor? The \(4.00 \cdot 10^{3}-\mathrm{nF}\) capacitor is then disconnected from the 12.0 - \(\mathrm{V}\) battery and used to charge three uncharged capacitors, a 100.-nF capacitor, a 200.-nF capacitor, and a 300.-nF capacitor, connected in series. c) After charging, what is the potential difference across each of the four capacitors? d) How much of the electrical energy stored in the \(4.00 \cdot 10^{3}-\mathrm{nF}\) capacitor was transferred to the other three capacitors?
A capacitor consists of two parallel plates, but one of them can move relative to the other as shown in the figure. Air fills the space between the plates, and the capacitance is \(32.0 \mathrm{pF}\) when the separation between plates is \(d=0.500 \mathrm{~cm}\) a) A battery supplying a potential difference \(V=9.00 \mathrm{~V}\) is connected to the plates. What is the charge distribution, \(\sigma,\) on the left plate? What are the capacitance, \(C^{\prime},\) and the charge distribution, \(\sigma^{\prime},\) when \(d\) is changed to \(0.250 \mathrm{~cm} ?\) b) With \(d=0.500 \mathrm{~cm}\), the battery is disconnected from the plates. The plates are then moved so that \(d=0.250 \mathrm{~cm}\) What is the potential difference \(V^{\prime}\) between the plates?
A 4.00 -pF parallel plate capacitor has a potential difference of \(10.0 \mathrm{~V}\) across it. The plates are \(3.00 \mathrm{~mm}\) apart, and the space between them contains air. a) What is the charge on the capacitor? b) How much energy is stored in the capacitor? c) What is the area of the plates? d) What would the capacitance of this capacitor be if the space between the plates were filled with polystyrene?
A parallel plate capacitor with a dielectric filling the volume between its plates is charged. The charge is a) stored on the plates. b) stored on the dielectric. c) stored both on the plates and in the dielectric.
The battery of an electric car stores 60.51 MJ of energy. If 6990 supercapacitors, each with capacitance \(C=3.423 \mathrm{kF}\), are required to supply this amount of energy, what is the potential difference across each supercapacitor?
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