IB DP Physics: HL复习笔记11.3.3 Capacitors in Series & Parallel

• Capacitors can be combined in series and parallel circuits
• The combined capacitance depends on whether the capacitors are connected in series or parallel

Capacitors in Series

• Consider two parallel plate capacitors C1 and C2 connected in series, with a potential difference  (p.d) V across them

Capacitors connected in series have different p.d across them but have the same charge

• In a series circuit, p.d is shared between all the components in the circuit
  • Therefore, if the capacitors store the same charge on their plates but have different p.ds, the p.d across C1 is V1 and across C2 is V2
• The total potential difference V is the sum of V1 and V2

V = V1 + V2

• Rearranging the capacitance equation for the p.d V means V1 and V2 can be written as:

• Where the total p.d V is defined by the total capacitance

• Substituting these into the equation V = V1 + V2 equals:

• Since the current is the same through all components in a series circuit, the charge Q is the same through each capacitor and cancels out
• Therefore, the equation for combined capacitance of capacitors in series is:

Capacitors in Parallel

• Consider two parallel plate capacitors C1 and C2 connected in parallel, each with p.d V

Capacitors connected in parallel have the same p.d across them, but different charge

• Since the current is split across each junction in a parallel circuit, the charge stored on each capacitor is different
• Therefore, the charge on capacitor C1 is Q1 and on C2 is Q2
• The total charge Q is the sum of Q1 and Q2

Q = Q1 + Q2

• Rearranging the capacitance equation for the charge Q means Q1 and Q2 can be written as:

Q1 = C1V     and      Q2 = C2V

• Where the total charge Q is defined by the total capacitance:

Q = CtotalV

• Substituting these into the Q = Q1 + Q2 equals:

CtotalV = C1V + C2V = (C1 + C2) V

• Since the p.d is the same through all components in each branch of a parallel circuit, the p.d V cancels out
• Therefore, the equation for combined capacitance of capacitors in parallel is:

Ctotal = C1 + C2 + C3 ...

Step 1: Calculate the combined capacitance of the two capacitors in parallel

Capacitors in parallel: Ctotal = C1 + C2 + C3 …

Cparallel = 23 + 35 = 58 μF

Step 2: Connect this combined capacitance with the final capacitor in series

Step 3: Rearrange for the total capacitance