Questions for Capacitance

 

A capacitor has initial capacitance C. A dielectric of dielectric constant 4 is pushed between the plates so that it covers a quarter of the capacitor’s area. What is the new capacitance in terms of C?

A capacitor is charged to 12V and disconnected from the battery. Its plates are then pushed together such that their new separation is half as big as initially. What is the new potential difference across the capacitor?

A capacitor is charged to 3V, 12 μF using a 3V power supply. It is then disconnected and re-connected to a 6V power supply, where it continues charging. Assuming that the capacitor does not break down, what is the work done as it charges from 3V to 6V?

A capacitor C1 of capacitance C is connected to a 12V source and allowed to charge fully. It is then disconnected from the source and connected with an uncharged identical capacitor C2. How much charge, in terms of C, is now on C2? What is the new potential difference across C1?

A capacitor C1 of capacitance C is connected to a 6V source and allowed to charge fully. It is then disconnected from the source and connected with an uncharged identical capacitance Cof capacitance C/2. How much charge, in terms of C, is now on C2?

A capacitor C1 of capacitance C is connected to a 10V source and allowed to charge fully. A capacitor C2 of capacitance 3C/4 is connected to a 12V source and allowed to charge fully.

  1. The two are then connected with their positively-charged plates touching. How much charge are on capacitors C1 and C2 each?
  2. Should the two have been connected with oppositely-charge plates touching, how much charge would have been on capacitors C1 and C2 each?

Three capacitors C1, C2, and C3 with respective capacitances of 6 μF, 12 μF and 10 μF are connected in series across a 14V supply.

  1. How much charge accumulates on C2?
  2. What is the potential difference across C3?

The three capacitors are now disconnected. C1’s positive plate is connected to touch C2’s negative plate. C3’s positive plate touches C2’s positive plate, and C3’s negative plate touches C1’s negative plate.

  1. What is the total capacitance of C1 and C2?
  2. How much charge accumulates on C3?
  3. What is the voltage across Cand Ccombined?
  4. What is the voltage across Calone?
  5. How much energy is stored in C1?

A uncharged capacitor of capacitance 6 μF is connected to a 6V battery and a 2Ω resistor. In the midst of charging, it holds 2.4·10-5 C of charge. How much time has passed since it began charging?

A capacitor of capacitance C and initial charge Qi is connected in series with a 6V power supply and a 2Ω resistor.

  1. What is the potential difference across the capacitor?
  2. Assume that the potential difference across the capacitor is smaller than 6V. Is the capacitor charging or discharging?

An uncharged capacitor of capacitance 6 μF is connected in series with a 10V power supply and a 3Ω resistor. What is the maximum amount of charge in can attain in this circuit? What is the time taken for it to charge up to half this amount?