Capacitance Circuit Homework: Initial Conditions

[unscientific]

Homework Statement

Initial Conditions
(a)
Switch S₂ kept open, switch S1 closed until C₁, C₂ and C₃ are fully charged. What is the potential difference across each capacitor? Now Switch S₂ is closed. What is the new potential difference across each capacitor?

(b) Switches S₁ and S₂ are both closed. What is the p.d. across each capacitor?

The Attempt at a Solution

(a)
Before S₂ is closed, p.d. across all 3 capacitors are the same:

V₁ = V₂ = V₃ = 80V
V₄ = 0V

After S₂ is closed, capacitors 2 and 3 do not affect the circuit at all hence they retain the p.d. of 80V.

C₁ distributes half of its charge to C₄.

V₂ = V₃ = 80V

C₁ = C₄ = 40V(b)

C₁ and C₄ are in parallel, so C_1,4 = 2C

thus it is C_1,4, C₂ and C₃ in series. Hence p.d. across each is:

V₂ = V₃ = 96V
V_1,4 = V₁ = V₄ = 48V

 

[mfb]

Looks correct. You could add the formula you used at (b).

 

[unscientific]

Looks correct. You could add the formula you used at (b).

Thanks!

 

[jfgobin]

Do all capacitors have the same capacitance?

If yes, then your answer is correct. If not, you must use the conservation of charge to calculate the potential difference for each capacitor.

J.

 

[SammyS]

By the way, this thread should be in the Introductory Physics section.

Homework Statement

Initial Conditions
(a)
Switch S₂ kept open, switch S1 closed until C₁, C₂ and C₃ are fully charged. What is the potential difference across each capacitor? Now Switch S₂ is closed. What is the new potential difference across each capacitor?

(b) Switches S₁ and S₂ are both closed. What is the p.d. across each capacitor?

The Attempt at a Solution

(a)
Before S₂ is closed, p.d. across all 3 capacitors are the same:

V₁ = V₂ = V₃ = 80V
V₄ = 0V

After S₂ is closed, capacitors 2 and 3 do not affect the circuit at all hence they retain the p.d. of 80V.

C₁ distributes half of its charge to C₄.

V₂ = V₃ = 80V

C₁ = C₄ = 40V

(b)

C₁ and C₄ are in parallel, so C_1,4 = 2C

thus it is C_1,4, C₂ and C₃ in series. Hence p.d. across each is:

V₂ = V₃ = 96V
V_1,4 = V₁ = V₄ = 48V

I'm assuming that initially, before either switch is closed all the capacitors are discharged.

Then S₁ is closed & S₂ is open, with C₁, C₂ and C₃ becoming fully charged.

At this point, each of the three capacitors is charged equally. If they all have the same capacitance, then they will each have the same p.d., as in your analysis.​

Then for part (a), S₁ is opened followed by S₂ being closed.

If capacitors, C₁ & C₄, have the same capacitance, then they will be charged equally.

If not, then you can use the fact that they will have the same p.d. to find the charge on each, keeping in mind to employ conservation of charge.​

For part (b): (Your answer is incorrect even if all the capacitances are equal.)

What is the equivalent capacitance of the 4 capacitors?

 

[berkeman]

Moved to Intro Physics.