Physics
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A physics student connects two identical parallel-plate capacitors with a capacitance of 4 μF to a battery with a voltage difference of 10 V, either in series or in parallel. The two plates are separated by a distance of 1mm. Determine i) the ratio of the energy stored (Useries/Uparallel). ii) the ratio of the maximum amount of charge stored (Qseries/Qparallel), and iii) the ratio of the electric field (Eseries/Eparallel) between the two plates.
A device composed of two identical parallel-conducting plates separated by a distance d is connected to a battery. The capacitance of this device is 430 pF. The charge on each plate is 1.45 µC when the voltage difference across the plates is V. i) Determine V. Consider the charge on each plate remaining constant. ii) What is the voltage difference across the plates if the separation distance is tripled (Vnew)? iii) Determine the work done in tripling the separation?
A battery with a potential difference of 12 V is connected to a parallel-plate capacitor without any dielectric within its plates. The capacitance of the capacitor is 12.85 μF. The plates are separated by a distance of 1.00 mm. When fully charged, what is the energy density stored between the plates in SI units?
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.
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 student adjusts the capacitance of an isolated parallel-plate capacitor with a charge of 500 μC from 8.5 μF to 3.5 μF by modifying the distance between the plates using an external force. Find the work done by the external force during this adjustment.
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.