CAPACITOR IN SERIES -
Capacitors are connected together in series when they are daisy-chained together in a single line.
→ In series-connected capacitors, the charging current ( iC ) flowing through the capacitors is the same for all capacitors as it only has one path to follow.
→ When capacitors are connected in series, the total capacitance is less than anyone of the series capacitors’ individual capacitances. If two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the sum total of the plate spacings of the individual capacitors. As we’ve just seen, an increase in plate spacing, with all other factors unchanged, results in decreased capacitance.
→ When Capacitors in Series all have the same current flowing through them as iT = i1 = i2 = i3 etc. Therefore each capacitor will store the same amount of electrical charge, Q on its plates regardless of its capacitance. This is because the charge stored by a plate of anyone capacitor must have come from the plate of its adjacent capacitor. Therefore, capacitors connected together in series must have the same charge.
QT = Q1 = Q2 = Q3 ….etc
Capacitor in series connection -
Consider the following circuit in which the three capacitors, C1, C2 and C3 are all connected together in a series branch across a supply voltage between point A and B.
In a series-connected circuit, however, the total or equivalent capacitance CT is calculated differently.
In the series circuit above the right-hand plate of the first capacitor, C1 is connected to the left-hand plate of the second capacitor, C2 whose right-hand plate is connected to the left-hand plate of the third capacitor, C3. Then this series connection means that in a DC connected circuit, capacitor C2 is effectively isolated from the circuit.
The result of this is that the effective plate area has decreased to the smallest individual capacitance connected in the series chain. Therefore the voltage drop across each capacitor will be different depending upon the values of the individual capacitance’s.
Then by applying Kirchhoff’s Voltage Law, ( KVL ) to the above circuit, we get:
Since Q = C*V and rearranging for V = Q/C, substituting Q/C for each capacitor voltage VC in the above KVL equation will give us:
dividing each term through by Q gives
The equivalent capacitance -
In a series-connected circuit, however, the total or equivalent capacitance CT is calculated differently.
In the series circuit above the right-hand plate of the first capacitor, C1 is connected to the left-hand plate of the second capacitor, C2 whose right-hand plate is connected to the left-hand plate of the third capacitor, C3. Then this series connection means that in a DC connected circuit, capacitor C2 is effectively isolated from the circuit.
The result of this is that the effective plate area has decreased to the smallest individual capacitance connected in the series chain. Therefore the voltage drop across each capacitor will be different depending upon the values of the individual capacitance’s.
Then by applying Kirchhoff’s Voltage Law, ( KVL ) to the above circuit, we get:
Since Q = C*V and rearranging for V = Q/C, substituting Q/C for each capacitor voltage VC in the above KVL equation will give us:
dividing each term through by Q gives
The equivalent capacitance -
Thus the capacitance of a series-connected capacitor is the reciprocal of the sum of the reciprocals of the individual capacitance
→ Note that capacitor in series combines in the same manner as a resistor in parallel.
Example no 1
Find the equivalent capacitance seen at the terminals of the circuit in fig.1.1.
fig. 1.1
solution-
The 20 μF and 4 μF capacitors are in series; their equivalent capacitance is
20*4/20+4 = 3.3μF
Example no 2 -
Find the equivalent capacitance seen at the terminals of the circuit in fig.1.2.
fig. 1.2
solution -
The 10 μF, 6 μF and 4μF capacitors are in series; so that equivalent capacitance is
10*6*4/10+6+4 = 12μF
Thus the capacitance of a series-connected capacitor is the reciprocal of the sum of the reciprocals of the individual capacitance
→ Note that capacitor in series combines in the same manner as a resistor in parallel.
Example no 1
Find the equivalent capacitance seen at the terminals of the circuit in fig.1.1.
fig. 1.1
solution-
The 20 μF and 4 μF capacitors are in series; their equivalent capacitance is
20*4/20+4 = 3.3μF
Example no 2 -
Find the equivalent capacitance seen at the terminals of the circuit in fig.1.2.
fig. 1.2
solution -
The 10 μF, 6 μF and 4μF capacitors are in series; so that equivalent capacitance is
10*6*4/10+6+4 = 12μF
Capacitors in Series Summary
Then to summarise, the total or equivalent capacitance, CT of a circuit containing Capacitors in Series is the reciprocal of the sum of the reciprocals of all of the individual capacitance’s added together.
Also for capacitors connected in series, all the series-connected capacitors will have the same charging current flowing through them as iT = i1 = i2 = i3 etc. Two or more capacitors in series will always have equal amounts of coulomb charge across their plates.
As the charge, ( Q ) is equal and constant, the voltage drop across the capacitor is determined by the value of the capacitor only as V = Q ÷ C. A small capacitance value will result in a larger voltage while a large value of capacitance will result in a smaller voltage drop.
Introduction of capacitor -
CAPACITOR TYPES
CAPACITOR CHARACTERISTICS
Then to summarise, the total or equivalent capacitance, CT of a circuit containing Capacitors in Series is the reciprocal of the sum of the reciprocals of all of the individual capacitance’s added together.
Also for capacitors connected in series, all the series-connected capacitors will have the same charging current flowing through them as iT = i1 = i2 = i3 etc. Two or more capacitors in series will always have equal amounts of coulomb charge across their plates.
As the charge, ( Q ) is equal and constant, the voltage drop across the capacitor is determined by the value of the capacitor only as V = Q ÷ C. A small capacitance value will result in a larger voltage while a large value of capacitance will result in a smaller voltage drop.
Introduction of capacitor -
CAPACITOR TYPES
CAPACITOR CHARACTERISTICS
Capacitor in series
Reviewed by Educatdeck
on
January 08, 2020
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Reviewed by Educatdeck
on
January 08, 2020
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