# Capacitors in Series & Parallel Circuits(OCR A Level Physics)

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Katie M

Expertise

Physics

## 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 ...

#### Solving Problems with Capacitors in Series & Parallel

• For capacitors in series:

• For capacitors in parallel:

#### Worked example

Three capacitors with capacitance of 23 μF, 35 μF and 40 μF are connected as shown below.

Calculate the total capacitance between points A and B.

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

#### Exam Tip

Both the combined capacitance equations look similar to the equations for combined resistance in series and parallel circuits. However, take note that they are the opposite way around to each other!

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