电容器in Series and Parallel

电容器是电子电路中的标准组件。电容器的不同组合实际上是在电路中使用的。本文解释了电容器的串联和平行组合。

串联电容器

如何连接电容器串联？

串联的电容器是指单线连接的两个或多个电容器。一个电容器的正板连接到下一个电容器的负板。

Here,

qt = q1 = q2 = q3 = ————- = q

IC = I1 = I2 = I3 = ——— = IN

当电容器以串联电荷连接时，所有电容器的电流相同。

为什么电容器的电荷相同？

For series capacitors same quantity of electrons will flow through each capacitor because the charge on each plate is coming from the adjacent plate. So, coulomb charge is same.As current is nothing but flow of electrons , current is also same.

What is the equivalent capacitance?

等效电容是电容器的总体电容。让我们看看如何在串联时计算电容。

Below is the figure showing three capacitors connected in series to the battery. When the capacitors are connected in series the adjacent plates get charged due to electrostatic induction.

Each plate will have different potential. But the magnitude of charge on the plates is same.

C1的第一板将具有电势V1，其电池电压和第二板的电势将小于V1。让它成为V2。

Now the first plate of C2 will have potential equal to V2 and second plate will have potential less than V3 let it be V4.
第一板C3具有电势V5（V5 = V4），第二板的电势小于V5。让它成为V6。

But the overall potential difference between the plates is equal to the emf of the battery.

So VT = V1+V2+V3

But we know that, Q=CV

c = q/v

Ceq = Q/V1 + Q/V2 + Q/V3 (As charge is same)

1/CEQ =（V1+ V2+ V3）/Q

VT = Q/Ceq = Q/C1 + Q/C2 + Q/C3

Hence,1/Ceq = 1/C1 + 1/C2 + 1/C3

If N capacitors are connected in series then equivalent capacitance can be given as below.

1/Ceq = 1/C1 + 1/C2 +……… + 1/CN

因此，当电容器处于串联连接时，等效电容的倒数等于电容器中电容器单个电容的倒数之和。

系列示例中的电容器

Calculate the equivalent capacitance and the individual voltage drops across the set of two capacitors in series have 0.1uF and 0.2uF respectively when connected to a 12V a.c. supply.

Equivalent capacitance,

1/Ceq = 1/C1 + 1/C2

Ceq = (C1C2) / (C1 + C2)

CEQ =（0.1UF*0.2UF） /（0.1UF+0.2UF）

Ceq = 0.066uF = 66nF

Voltage drops across the two given capacitors in series are,

V1 = (C2*VT)/ (C1+C2) = (0.2uF*12V)/ (0.1uF+0.2uF) = 8Volts

V2 =（C1*VT）/（C1+C2）=（0.1UF*12V）/（0.1UF+0.2UF）= 4Volts

From these results we observed that the equivalent capacitance 66nF is less than the smallest capacitance 0.1uF of the given two capacitors. The individual voltage drops across the given two capacitors are different.

但是两个电容器的单个电压降和等于总电压。即8V+4V = 12V。

现在，我们计算存储在单个电容器中的电荷，

Q1 = V1* C1 = 8V * 0.1uF = 0.8uC

Q2 = V2 * C2 = 4V * 0.2UF = 0.8UC

Here we observed that equal charge 0.8uC is stored in both the capacitors C1 and C2 which are connected in series.

电容器in Series Summary

•在串联连接中，电容器上的充电相同。

• Equivalent capacitance of the capacitors is less than the smallest capacitance in series.

•n个电容器的等效电容串联为

1/Ceq = 1/C1 + 1/C2 +……… + 1/CN

电容器in Parallel Circuits

Why do we connect capacitors in parallel?

There is an advantage of connecting capacitors in parallel than in series. When the capacitors are connected in parallel the total capacitance value is increased. There are some applications where higher capacitance values are required.

How to connect capacitors in Parallel?

下图显示了平行电容器的连接。所有正终端都连接到一个点，负端子连接到另一点。

平行电容器的等效电容是什么？

• All the capacitors which are connected in parallel have the same voltage and is equal to the VT applied between the input and output terminals of the circuit.
• 然后，平行电容器在它们上都有“公共电压”供应。vt = v1 = v2等
• 平行连接电容器的电路的等效电容，等于加在一起添加的电容器的所有单个电容的总和。
• This is because the top plate of each capacitor in the circuit is connected to the top plate of adjacent capacitors.In the same way the bottom plate of each capacitor in the circuit is connected to the bottom plate of adjacent capacitors.

让我们看看如何在并行连接时计算电容器的等效电容。考虑两个电容器，如下电路所示。

总负责整个电路划分(Q)between the two capacitors, means the charge Q distributes itself between the capacitors connected in parallel. charge Q is equal to the sum of all the individual capacitor charges.

因此Q = Q1+Q2

Where Q1,Q2 are charges at capacitors C1 And C2.

We know that,

Q=Ceq VT

Here, Q = Q1+Q2

CEQ VT = C1XV1+C2XV2

Since VT = V1 = V2 = V

CEQ VT = C1XV+C2XV

CEQ VT =（C1+C2）V

Hence Ceq=C1+c2

If N capacitors are connected in parallel then Ceq=C1+C2+C3+——Cn

Thus equivalent capacitance of the capacitors which are connected in parallel is equal to the sum of the individual capacitance of the capacitors in the circuit.

电容器in Parallel Example No1

Consider the capacitance values of the two capacitors C1 =0.2uF and C2 =0.3uF which are shown in above figure 4. Now calculate the equivalent capacitance of the circuit.

We know that the Equivalent capacitance,

CEQ = C1 + C2

Ceq =0.2uF + 0.3uF

CEQ = 0.5UF

要记住并行连接电容器电路的一个重要点，即并行连接的任何两个或多个电容器的等效电容（CEQ）将始终大于电路中最大电容器的值，因为我们正在加在一起。因此，在我们上面的示例中，CEQ = 0.5UF，而电路中最大的值电容器仅为0.3UF。

When capacitors are connected in parallel?

Here are some applications where capacitors are connected in parallel.

• 在某些DC供应中，使用了更好地过滤带有上波纹因子的小电容器。这些并行连接以增加电容值。
• This can be used in automotive industries in large vehicles like trams for regenerative braking. These application may require large capacitance values than the capacitance usually available in the market.

电容器in parallel Summary

• 平行连接时电容器上的电压相同。平行电容器的等效电压等于并行的最小电压额定电容器。
• 电容器的总电容值是并联连接的所有电容值的总和。
• Equivalent capacitance of n capacitors in parallel is Ceq=C1+C2+C3…Cn.