# Worksheet: Capacitance of a Parallel Plate Capacitor

In this worksheet, we will practice calculating the capacitance of two parallel charged plates given their surface area and the distance between them.

Q1:

The plates of an empty parallel plate capacitor of capacitance 5.0 pF are 2.0 mm apart. What is the area of each plate?

• A m2
• B
• C
• D m2
• E m2

Q2:

An air-filled (empty) parallel plate capacitor is made from two square plates whose sides are 25 cm and are 1.0 mm apart. The capacitor is connected to a 50 V battery and is fully charged. It is then disconnected from the battery and its plates are pulled apart to a separation of 2.00 mm.

What is the capacitance of this new capacitor?

What is the charge on each plate?

What is the electrical field between the plates?

Q3:

An anxious physicist worries that the two metal shelves of a wood frame bookcase might obtain a high voltage if charged by static electricity, perhaps produced by friction. The shelves have an area of 1.00 m2 and are separated by a distance of 0.200 m. A total charge of 2.00 nC is placed on the two shelves.

What is the capacitance of the shelves?

• A F
• B F
• C F
• D F
• E F

What is the potential difference across the shelves?

How much energy is stored in the electric field between the shelves?

• A J
• B J
• C J
• D J
• E J

Q4:

An 8.0 pF vacuum capacitor has a plate area of 0.070 m2. What is the separation between its plates?

Q5:

Two parallel conducting plates, each of cross-sectional area 580 cm2, are 3.2 cm apart and uncharged. electrons are transferred from one plate to the other.

What is the charge density on each plate?

• A C/m2
• B C/m2
• C C/m2
• D C/m2
• E C/m2

What is the magnitude of the electric field between the plates?

• A N/C
• B N/C
• C N/C
• D N/C
• E N/C

Q6:

A capacitor is made from two flat parallel plates placed 1.9 mm apart. When a charge of 0.040 µC is placed on the plates, the potential difference between them is 360 V.

What is the capacitance of the plates?

What is the area of each plate?

What is the charge on the plates when the potential difference between them is 850 V?

What is the maximum potential difference that can be applied between the plates so that the magnitude of the electric field between the plates does not exceed 4.5 MV/m?

Q7:

An empty parallel plate capacitor has a capacitance of 80 µF. How much charge must leak off its plates before the voltage across them is reduced by 250 V?

Q8:

A parallel plate capacitor with a capacitance of 8.0 µF is charged with a 0.5 V battery, after which the battery is disconnected. What is the minimum work required to increase the separation between the plates by a factor of 5?

Q9:

A parallel plate capacitor is made of two square plates that have sides 13.5 cm long, separated by a distance of 1.0 mm. The capacitor is connected to a 28 V battery. With the battery still connected, the plates are pulled away from each other until they are separated by 1.2 mm.

What is the energy stored in the capacitor before the plates are pulled farther apart?

• A32 nJ
• B130 nJ
• C63 nJ
• D74 nJ
• E19 nJ

What is the energy stored in the capacitor after the plates are pulled farther apart?

• A110 nJ
• B53 nJ
• C27 nJ
• D81 nJ
• E47 nJ

Q10:

Two flat plates containing equal and opposite charges are separated by material 3.0 mm thick with a dielectric constant of 6.0. Take the electric field in the dielectric to be 6.0 MV/m.

What is the charge density on the capacitor plates?

What is the induced charge density on the surfaces of the dielectric?

Q11:

A parallel-plate capacitor has plates of area 0.50 m2 that are separated by 0.60 m. The potential difference across the plates varies with time and is modeled as . What is the displacement current between the capacitor’s plates at the instant ?

• A A
• B A
• C A
• D A
• E A

Q12:

Two parallel plates have equal and opposite charges. When the space between the plates is evacuated, the electrical field is . When the space is filled with a dielectric, the electrical field is .

What is the surface charge density on each surface of the dielectric?

What is the dielectric constant?