Four capacitors with capacitances C1 = 12 µF, C2 = 6 µF, C3 = 6 µF, and C4 = 12 µF are wired to a battery with a potential difference of 8 V as shown in the figure. What is the total charge (Q) stored on the four capacitors?
Consider two capacitors: the first capacitor has a capacitance (C1) of 850 nF, and the second capacitor has a capacitance (C2) of 400 nF. Initially, these capacitors are charged individually using a 14 V battery. The capacitors are isolated from the battery, maintaining the charge on the capacitor plates unchanged. Next, the two capacitors are connected in parallel, with the positive plate of each capacitor connected to the negative plate of the other capacitor. Determine the charge on each capacitor and the voltage difference across the capacitors when they are connected in parallel.
A plane capacitor consists of two parallel circular plates with a radius of 4.0 cm. The plates are separated by a distance of 0.20 mm. The capacitor is charged to a potential difference of 120 volts. Calculate the i) total energy stored and ii) energy density within the electric field of the charged plane capacitor.
During an experiment, a parallel plate capacitor is used to launch a 4.5 g ball vertically upwards by converting the electrical energy to mechanical energy. The capacitor, initially charged to a voltage of 145 V, undergoes an ultrafast discharge, propelling the ball to a height of 2.8 m. Determine the capacitance of the capacitor, neglecting any dissipation effect.
A 6.5 μF capacitor, initially without any charge, undergoes a uniform charging process and stores energy at a rate of (300 W)×t, where t is the time in seconds. Determine the voltage across the capacitor after 3.5 μs of charging.
A capacitor used in a medical device stores 300 J of energy within a cube-shaped region with side lengths of 7.0 cm, in a region characterized by a constant electric field. Calculate the magnitude of the electric field assuming a dielectric constant of 110 between the plates.
A paper slab is inserted between the plates of an air-filled parallel plate capacitor. The space between the plates is completely filled by the paper slab. The dielectric constant K and dielectric strength of the paper slab are 3.7 and 1.6 × 107 V/m, respectively. i) Find the energy density stored in the capacitor if the electric field between the plates is 1/4 of the dielectric strength. ii) The capacitor is attached to a 100.0 V power source that maintains a constant electric field equal to 1/4 of the dielectric strength between the plates. The energy stored in the capacitor is 12.5 µJ. Find the area of the plates.
