Each segment will have different potential. But the amount of charge on the plate is the same.
The first plate of C1 has a potential V1 equal to the voltage of the battery, and the second plate has a potential less than V1, which we call V2.
Now the potential of the first board of C2 is equal to V2, and the potential of the second board is less than V3, so let's call it V4.
The first plate of C3 has a potential of V5 (V5=V4), and the second plate has a potential less than V5, which we call V6. But the total potential difference between the plates is equal to the electromotive force of the battery.
So VT is equal to V1 plus V2 plus V3, but we know that Q is equal to CV
C=Q/V
Ceq = Q/V1 + Q/V2 + Q/V3 (same charge)
1/Ceq = (V1+ V2+ V3)/Q
VT = Q/Ceq = Q/C1 + Q/C2 + Q/C3
So 1/Ceq = 1/C1 + 1/C2 + 1/C3
If N capacitors are in series, the equivalent capacitance is as follows.
1/Ceq = 1/C1 + 1/C2 +………… + 1/CN
Therefore, when capacitors are connected in series, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocal of the individual capacitors in the circuit.
Capacitor Series Summary
• The electric charges on the capacitors connected in series are the same.
• The equivalent capacitance of the capacitor is less than the minimum capacitance in series.
• The equivalent capacitance of n series capacitors is
1/Ceq = 1/C1 + 1/C2 +………… + 1/CN
Capacitors In Parallel
Why Do We Need Parallel Capacitors?
Capacitors in parallel have one advantage over those in series. When capacitors are connected in parallel, the total capacitance value increases, and some applications require higher capacitance values.
How Do Capacitors Connect In Parallel?
The following diagram shows the parallel connection of the capacitors. All the positive terminals are connected to one point and the negative terminals are connected to another point.
What Is The Equivalent Capacitance OF The Parallel Capacitor?
All capacitors in parallel have the same voltage and are equal to the VT applied between the input and output terminals of the circuit.
The shunt capacitors then have a "common voltage" power supply between them. So VT = V1 = V2 and so on.
The equivalent capacitance Ceq of a capacitor parallel circuit is equal to the sum of the individual capacitors of all capacitors added together.
This is because the top plate of each capacitor in the circuit is connected to the top plate of the adjacent capacitor. In the same way, the baseboards of each capacitor in the circuit are connected to the baseboards of adjacent capacitors.
The following are some applications of capacitor parallel.
In some DC power supplies, small capacitors with excellent ripple coefficients are used for better filtering. These are connected in parallel to increase capacitance values.
This can be used for large vehicles in the automotive industry, such as trams. These applications may require larger capacitance values than are typically available on the market.
Shunt Capacitor Summary
The voltage across the capacitor is the same in parallel. The equivalent voltage of a shunt capacitor is equal to the minimum rated voltage capacitor in parallel.
The total capacitance value of a capacitor is the sum of all the parallel capacitance values.
The equivalent capacitance of n parallel capacitors is Ceq=C1+C2+C3... Cn.