27.8
多重电压源
通常，单个电池不足以为某些设备供电。 在这种情况下，电池可以通过两种方式组合：串联或并联。
串联时，一个电池的正极端子连接到另一个电池的负极端子。 因此，每个电池的电压相加得到净电压，净电压增加是因为每个电池都会增强进入它的电子。 由于串联连接，每个电池流过相同的电流。
电池串联是为了提高负载的端电…
当两个电池与一个负载电阻串联时，总电动势等于各个电池电动势之和。总内阻等于各个电池内阻之和。通过每个电池的电流相同。
端电压是各个端电压的总和。基尔霍夫回路定律给出了电流。
尽管串联连接会提高供电电压，但也会增加等效内阻。
串联的 N 个电池的等效端电压可以进行推广。
当两个电动势相同的电池并联连接至一个负载电阻时，总电动势与单个电池的电动势相同。
在公共节点处应用基尔霍夫电流定律，对回路1和回路2分别应用基尔霍夫电压定律，通过求解方程组可确定流经等效电阻的负载电流，从而得到端电压。
并联连接可降低内阻，并能产生较大的电流。
对于并联的 N 个电池，等效端电压表达式可以推广。
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Q1: What happens to voltage when batteries are connected in series?
When batteries are connected in series, the overall electromotive force (EMF) is the sum of individual batteries' EMFs. Each battery boosts the electrons flowing through it, resulting in increased total voltage. For example, two 1.5 V batteries in series produce 3.0 V. However, the total internal resistance also increases because internal resistances are additive in series configurations.
Q2: How does parallel connection of batteries differ from series connection?
In parallel connection, positive terminals connect together and negative terminals connect together, maintaining the same EMF as individual batteries. Parallel configuration reduces equivalent internal resistance, allowing larger current delivery to the load. This setup is ideal for high-current applications like diesel truck engines, where two 12 V batteries in parallel provide 12 V but deliver greater current capacity.
Q3: Why is internal resistance important when combining voltage sources?
Internal resistance affects the terminal voltage available to the load. In series, internal resistances add, reducing efficiency. In parallel, internal resistance decreases, enabling higher current output. Terminal voltage equals EMF minus the product of equivalent internal resistance and current. Lower internal resistance in parallel configurations allows batteries to deliver more power to devices requiring high current.
Q4: What determines the current flow through batteries in series?
Kirchhoff's loop rule determines the current in series circuits. The same current flows through each battery because they are connected in series. The current is calculated using the total EMF divided by the total resistance, which includes both the load resistor and the sum of all internal resistances from each battery.
Q5: How do you calculate terminal voltage for multiple batteries in parallel?
Terminal voltage for parallel batteries equals the EMF minus the equivalent internal resistance multiplied by the load current. Applying Kirchhoff's junction and loop rules at common nodes determines the load current through equivalent resistance. Since parallel connection reduces internal resistance compared to individual batteries, the terminal voltage remains close to the EMF even under load.
Q6: When should batteries be connected in series versus parallel?
Connect batteries in series to increase voltage for devices requiring higher voltage, like flashlights needing 3.0 V from two 1.5 V cells. Connect batteries in parallel to increase current capacity and runtime for high-power devices like diesel engines. Series increases voltage but internal resistance; parallel maintains voltage while reducing internal resistance and enabling larger current delivery.
Q7: How can you generalize the EMF and resistance for N batteries in series or parallel?
For N batteries in series, total EMF is the sum of all individual EMFs, and total internal resistance is the sum of all individual internal resistances. For N identical batteries in parallel, total EMF equals one battery's EMF, while equivalent internal resistance is one battery's internal resistance divided by N. These generalizations allow prediction of voltage and current for any number of combined batteries.