Energy Stored by Capacitor Practice Problems

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 (V_new)? 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 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.

In an advanced electronics workshop, engineers are designing a sensor that uses a parallel-plate air capacitor. The two plates are separated by a distance of 1.20 mm. When a potential difference of 250.0 V is applied, the charge on each plate is measured to be 0.0250 µC. (i) Calculate the capacitance of the air capacitor. (ii) Determine the surface area of each plate. (iii) Find the maximum voltage that can be applied without causing dielectric breakdown, given that the dielectric strength of air is $3.00\times 10^6\mathrm{~V}/\mathrm{m}$. (iv) Compute the total energy stored in the capacitor when the charge on the plates is 0.0250 µC.

A circuit contains two capacitors. The first is a 400 μF capacitor initially charged to 200 V, while the second is an uncharged 1400 μF capacitor. Both are connected to open switches. What maximum voltage value could be achieved on this uncharged capacitor by correctly operating both switches?

Two rectangular metal plates, each measuring 10.0 cm by 10.0 cm, are separated by an air gap of 2.0 mm. If the plates are oppositely charged with a charge magnitude of 500 μC, how much energy is stored in the electric field between them?

A large 4.0-F capacitor is used to power a heating device that raises the temperature of 1.0 kg of ethanol from 20°C to 70°C. What voltage must be applied across the capacitor's plates to achieve this temperature increase?

In a laboratory demonstration, the instructor fully charges a 3.0-μF capacitor by connecting it across a 12.0-V DC voltage source. After a day, half of its energy stored gets lost due to charge leakage. What is the amount of charge lost?

A parallel plate capacitor is connected to a battery that maintains a constant voltage of "V". A dielectric slab with dielectric constant "κ" is inserted between the plates. You need to remove the dielectric slab while the battery remains connected. How much work is required to remove the slab under these conditions?

Inside a parallel-plate capacitor, the electric field is approximately 2000 N/C.

i. What is the energy density between the plates of the capacitor?

ii. Estimate the total electric energy stored in the capacitor if the plate area is 0.02 m² and the separation between the plates is 5 mm.

iii. Compare (by a ratio) the answer to part ii with the energy needed to power a 100-watt light bulb for 1 hour.

Hint: The permittivity of free space $\epsilon _0$ = 8.85 × 10^-12 C²/(N·m²).

The energy stored by a charged capacitor in a defibrillator can be expressed as either $\frac12CV^2$ or $\frac12\frac{Q^2}{C}^{}$. The first expression shows that the energy depends directly on the capacitance C, while the second expression shows that the energy depends inversely on C.

i. How can these two different expressions accurately describe the energy stored in the capacitor? Explain.

ii. The first expression would be used in which scenario, and the second expression in which other scenario?

A regenerative braking system in an electric vehicle charges a 0.050 μF capacitor to a maximum voltage of 30 kV.

i. Determine the energy stored in the capacitor when it is fully charged.

ii. During braking, the motor is powered by 20% of the stored energy for 5.0 μs. Calculate the power output of the motor during this time.

You are working with a cylindrical capacitor in a laboratory. The capacitor consists of two concentric cylindrical shells: the inner cylinder has a radius of 0.50 cm, and the outer cylinder has a radius of 3.5 cm. These cylinders are maintained at a potential difference of 625 V, with the inner cylinder at a higher potential. Your task is calculating the energy stored in a 1.0-meter-long section of this cylindrical capacitor. [Hint: Capacitance = 2πϵ₀L / ln(R₂ / R₁), ϵ₀​ = 8.85 × 10⁻¹² F/m]

In an electronics laboratory, a student attempts to make a parallel plate capacitor. He takes two similar conducting parallel plates and keeps them 4.0 mm apart. He then charges them with a DC voltage source of 250 V. Afterward, he disconnects the voltage source and inserts between them a dielectric sheet (K = 2.5) with a surface area equal to that of the parallel plates but with a thickness of 2.0 mm. Calculate the percentage of the stored energy in the electric field inside the dielectric sheet.

Calculate the energy spent and the amount of charge transferred if two uncharged capacitors of capacitances 0.75-μF and 0.35-μF were completely charged using a 9.0 V battery, given that the capacitors were connected (i) in parallel and (ii) in series.

A parallel-plate capacitor is connected to a 50.0-V battery and has a dielectric with a dielectric constant of 3.0 inserted between its plates. The area of the plates is 0.25 m² each and they are separated by a distance of 2.0 mm. Determine the work required to remove the dielectric with the capacitor kept connected to the battery.