Unit 4: Capacitance and Dielectrics
How much charge a pair of conductors can hold at a given voltage, what happens wiring several together, and how slipping in an insulator changes the answer.
7 topics · 26 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Capacitors and Capacitance
- How it worksHow does capacitance relate the charge stored on a capacitor to the voltage across its two plates?
- Worked exampleFind the charge stored on a 5 microfarad capacitor connected across a 12 volt battery.
- Common mistakeWhy doesn't doubling the charge sitting on a capacitor also double that capacitor's own capacitance?
Your turn1 of 2
Find the charge stored on a 14 microfarad capacitor connected across a 17 volt battery.The Parallel-Plate Capacitor
- How it worksHow does a parallel-plate capacitor's capacitance come out of the field between the plates and their geometry?
- Worked exampleFind the capacitance of two 0.02 square meter plates separated by 1 mm with vacuum between them.
- Worked exampleFind the charge stored on that same capacitor once it's connected to a 9 volt battery.
- Going furtherWhat happens to a parallel-plate capacitor's capacitance if the plate separation is cut in half?
- Common mistakeWhy doesn't a parallel-plate capacitor's own capacitance depend at all on the voltage connected across it?
Your turn1 of 2
Find the capacitance of two plates, each of area 363 square centimeters, separated by 7 mm, with vacuum between them. Use epsilon0 = 8.85x10−12 C2/(N m2).Capacitors in Series
- How it worksHow do capacitors in series end up sharing the same charge while splitting up the total voltage?
- Worked exampleFind the equivalent capacitance of a 4 microfarad and a 12 microfarad capacitor connected in series.
- Common mistakeWhy don't series capacitors simply add their capacitances the way series resistors add their resistances?
Your turn1 of 2
Find the equivalent capacitance of a 14 microfarad and a 13 microfarad capacitor connected in series.Capacitors in Parallel
- How it worksHow do capacitors in parallel end up sharing the same voltage while splitting up the total charge?
- Worked exampleFind the equivalent capacitance of a 3, a 6, and a 9 microfarad capacitor connected in parallel.
- Ties togetherHow does the way capacitors combine in series and parallel end up as the mirror image of how resistors combine?
Your turn1 of 2
Find the equivalent capacitance of a 14, a 13, and a 19 microfarad capacitor connected in parallel.Energy Stored in a Capacitor
- How it worksHow does integrating the work to move charge onto a capacitor give an energy of one half C V squared?
- Worked exampleFind the energy stored in a 10 microfarad capacitor charged to 200 volts.
- Common mistakeWhy isn't the energy stored on a capacitor simply its charge times its voltage, with no factor of one half?
- Going furtherWhat happens to the energy stored in a capacitor if the voltage across it is doubled?
Your turn1 of 2
Find the energy stored in a 35 microfarad capacitor charged to 196 volts.Capacitors with Dielectrics
- How it worksHow does a dielectric's own internal polarization partly cancel the field sitting between the plates?
- Worked exampleFind the new capacitance of a 4 microfarad capacitor after a dielectric constant of 5 is inserted.
- Common mistakeWhy doesn't a dielectric slipped between the plates let charge actually flow across the gap between them?
- Going furtherWhat happens to the voltage across an isolated, already-charged capacitor once a dielectric is inserted?
- Worked exampleFind the energy stored in a 4 microfarad capacitor with a dielectric constant of 5, charged to 100 volts.
Your turn1 of 2
Find the new capacitance of a 14 microfarad capacitor after a dielectric constant of 7 is inserted.The Molecular Model of a Dielectric
- How it worksHow does an external field twist the polar molecules inside a dielectric into partial alignment?
- How it worksWalk me through how those aligned molecules create a weaker field that opposes the original one.
- Ties togetherHow does this molecular picture explain why a dielectric constant always comes out greater than one?
Your turn1 of 2
An insulating dielectric has no free charges able to move through it, yet it responds when placed in an external electric field. What actually happens inside the material?