Capacitors & Capacitance Practice Problems

Work out the capacitance of the copper balls in the drawing below.

Determine the charge on each metal plate measuring 3.0 cm × 3.0 cm, placed 2.0 mm apart and connected to a 12 V battery. Also, find the potential difference between them.

A pair of copper electrodes, each with a diameter of 4.0 cm, are separated by 0.70 mm. What is their capacitance if these electrodes are connected to a 200 V power supply?

A pair of copper electrodes, each with a diameter of 5.0 cm, are separated by 0.80 mm. What is the magnitude of the charge on each electrode if these electrodes are connected to a 300 V power supply?

A coaxial cable has an internal conductor with a radius of 1 mm and an external conductor with a radius of 3 mm. The voltage difference between them is set to be -500 V. What is the electric field at the surface of the internal conductor?

A capacitor with an air gap has a capacitance of 0.90 μF and a separation distance of 3.0 mm between its plates. If each plate carries a charge of 88 μC, determine the strength of the electric field between the plates.

A high-precision measurement device uses a long cylindrical capacitor consisting of four concentric metallic cylinders with radii 𝑅₁, 𝑅₂, 𝑅₃, and 𝑅₄. In this setup, all cylinders are made of copper. The cylinders Copper strips connect 2 and 3 to ensure they are at the same potential. Calculate the capacitance per unit length of this arrangement, assuming equal and opposite charges are placed on the innermost cylinder 𝑅₁ and the outermost cylinder 𝑅₄. The capacitance of the cylindrical capacitor is $C=\frac{2\pi \epsilon _0\ell }{\ln \left(\frac{R_{outer}}{R_{inner}}\right)}$.

What would be the capacitance if two rectangular plates with dimensions as length = 7.0 cm and breadth = 4.0 cm are separated by a distance 'd' equal to '3.0 mm' using oil as dielectric material? [The dielectric constant for oil is 3.0.]

Determine the charge on a parallel plate capacitor with a plate area of 5.0 cm² that is connected to a power source with a potential difference of 15 V until it's fully charged and disconnected from the power source. Consider an air-gap separation of 0.75 mm.

When a potential difference of 850 V is applied across a capacitor's plates, they hold charges of +2500 μC and -2500 μC respectively. What is the value of its capacitance?

A 15 μF capacitor is connected to a simple circuit with a battery and the capacitor only. If the fully charged capacitor plates carry a charge of 45 μC, find the battery's emf.

As a scientist exploring Mars for human habitation, you must find its capacitance. Assume Mars is a spherical conductor. The radius of Mars is 3.4 × 10⁶ m.

A physicist is experimenting with capacitors. She takes two similar capacitors and connects them in parallel. Later, she connects the combination to a voltage source, V_i. As a result, each of them is charged with an equal charge of Q_i. Afterwards, she disconnects the voltage source and puts in a dielectric medium with a dielectric constant of K = 2.5 between one of the capacitors. What would be the final voltage across the capacitors?

You have a capacitor with capacitance C. The left plate is grounded, and the right plate is connected to a source of alpha particles. Each alpha particle carries a charge of +2e. If N alpha particles land on the right plate, what is the resulting potential difference V across the capacitor?

In a portable power bank, each storage cell contains a capacitor used for energy storage. Each of these cells can store a small amount of charge that corresponds to a specific energy level. When the capacitor, with a capacitance of 50 fF (1 fF = 10⁻¹⁵ F), is charged to 2.0 V, it represents a fully charged state. Determine the number of excess electrons on the negative plate of the capacitor when it is fully charged.

Researchers are using a capacitor with capacitance C connected to a proton source. Their voltage-measuring device can detect changes of 2.0 mV. What value of capacitance C is needed to detect the voltage change from a single proton (1.6 × 10⁻¹⁹ coulombs) given a 2.0 mV change?

A remote off-grid cabin is powered by a wind turbine that generates 60 kW of power during peak wind conditions. Over the course of 8.0 hours, the turbine generates a total of approximately 1.7 x 10⁹ joules of energy. This energy needs to be stored in a battery bank made from lithium-ion cells.

(i) If the voltage of the battery bank is limited to 12 V, and each lithium-ion cell has a capacitance of 2.0 F per gram, how many kilograms of lithium-ion cells would be required to store this energy?

(ii) Given that the cabin's structural capacity can support a maximum additional mass of 500 kg, is it practical to use this battery bank for energy storage?

A glass slab of thickness t (dielectric constant $\kappa$) is placed between the plates of a parallel-plate capacitor. The plate separation is D, and the area is A. If t = 0.50D and κ = 5.0, by what factor does the capacitance change? Hint: Determine the new capacitance first.

You are analyzing a parallel-plate capacitor with a plate area A and separation d. The capacitor is partially filled with a dielectric material of thickness t and dielectric constant k, which does not touch the plates and extends beyond their edges. What is the net capacitance C _net​ of the capacitor in terms of A, d, t, and k, considering the division of the capacitor into regions and the effect of the dielectric material?

A metal sphere has a capacitance of "C" which is measured in units of pF. Given that the sphere has a radius of "R" in units of cm, estimate the numerical value of "C."

In a lab, a cylindrical capacitor has a 2.0 mm radius hollow inner conductor and an 8.0 mm radius outer shell. The inner conductor is positively charged, and the outer shell is negatively charged.

Determine the electric field (a) inside the inner conductor and (b) outside the outer shell.