Capacitors can be connected in series or in parallel. If a set of capacitors is connected in a circuit, the type of capacitor connection is related to the voltage and current values in that network.
The combination is connected across the battery to apply a potential difference (V) and charge the plates (Q). We can define the equivalent capacitance of the combination between two points
There are mainly two methods used for combining capacitors
- Series Combination
- Parallel Combination
Series Combination of Capacitors
When some capacitors are connected in series, The charge Q on each capacitor has the same magnitude. The potential difference between C1, C2, and C3 is different i.e. V1, V2, and V3. consider three capacitors of different values.
Capacitance in Series Circuit
When the capacitance of a network whose capacitors are in series is considered, the reciprocal of the capacitances of all the capacitors are added up to get the inverse of the total capacitance. To get it more clearly,
where C1 is the capacitance across the first capacitor, C2 is the capacitance across the second capacitor and C3 is the capacitance across the third capacitor in the above network.
Voltage in Series Circuit
The voltage across each capacitor depends on the value of the individual capacitance. Which means
The total voltage across the series capacitor circuit,
Where V1 is the voltage across the first capacitor, V2 is the voltage across the second capacitor and V3 is the voltage across the third capacitor in the above network.
Current in Series Circuit
The total amount of current flowing through a set of capacitors connected in series is the same at all points. Hence capacitors will store the same amount of charge regardless of their capacitance value.
Where I1 is the current through the first capacitor, I2 is the current through the second capacitor and I3 is the current through the third capacitor in the above network.
Charges in Series Circuit
Since the current is equal, the storage of charge is the same because any plate of the capacitor receives its charge from the adjacent capacitor and hence the capacitors in series will have the same charge.
Parallel Combination of Capacitors
When some capacitors are connected in parallel, The potential difference V between each is the same, and the charge on C1, and C2 is different, i.e. Q1 and Q2.
Capacitance in Parallel Circuit
The total capacitance of the circuit is equal to the sum of the individual capacitances of the capacitors in the network.
where C1 is the capacitance across the first capacitor, C2 is the capacitance across the second capacitor and C3 is the capacitance across the third capacitor in the above network.
Voltage in Parallel Circuit
The voltage measured at the end of the circuit is the same as the voltage across all capacitors connected in parallel circuits.
Where V1 is the voltage across the first capacitor, V2 is the voltage across the second capacitor and V3 is the voltage across the third capacitor in the above network.
Current in Parallel Circuit
The total current is equal to the sum of the currents flowing through each capacitor connected in a parallel network.
Where I1 is the current through the first capacitor, I2 is the current through the second capacitor and I3 is the current through the third capacitor in the above network.