Capacitor and Inductors are in series and parallel

 Capacitors in Series

• Capacitors are connected together in series when they are daisy chained together in a single line
• 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 any one 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

 

Capacitors in Series Example No1

Capacitors in Parallel

• Capacitors are connected together in parallel when both of its terminals are connected to each terminal of another capacitor
• When capacitors are connected together in parallel the total or equivalent capacitance, CT in the circuit is equal to the sum of all the individual capacitors added together. This is because the top plate of capacitor, C1 is connected to the top plate of C2 which is connected to the top plate of C3 and so on.
• The same is also true of the capacitors bottom plates. Then it is the same as if the three sets of plates were touching each other and equal to one large single plate thereby increasing the effective plate area in m2.
• Since capacitance, C is related to plate area ( C = ε(A/d) ) the capacitance value of the combination will also increase. 

Capacitors in Parallel Example No1

Calculate the total equivalent circuit capacitance CT as being:

CT = C1 + C2 + C3 = 0.1uF + 0.2uF + 0.3uF = 0.6uF

Inductors in Series

• In the Resistors in Series tutorial we saw that the different values of the resistances connected together in series just “add” together and this is also true of inductance.
• Inductors in series are simply “added together” because the number of coil turns is effectively increased, with the total circuit inductance LT being equal to the sum of all the individual inductances added together.
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Inductors in Series Example No1

Three inductors of 10mH, 40mH and 50mH are connected together in a series combination with no mutual inductance between them. Calculate the total inductance of the series combination.

Inductors in Parallel

• Inductors are said to be connected together in Parallel when both of their terminals are respectively connected to each terminal of another inductor or inductors
• The voltage drop across all of the inductors in parallel will be the same. Then, Inductors in Parallel have a Common Voltage across them

 

Inductors in Parallel Example No1

Three inductors of 60mH, 120mH and 75mH respectively, are connected together in a parallel combination with no mutual inductance between them. Calculate the total inductance of the parallel combination in millihenries.