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Generell reicht eine einzelne Batterie nicht aus, um einige Geräte mit Strom zu versorgen. In solchen Fällen können Batterien auf zwei Arten kombinier…
Wenn zwei Batterien mit einem Lastwiderstand in Reihe geschaltet werden, ist die Gesamt-EMK die Summe der EMK der einzelnen Batterien. Der Gesamtinnenwiderstand ist die Summe der einzelnen Innenwiderstände. Durch jede Batterie fließt derselbe Strom.
Die Klemmenspannung ist die Summe der einzelnen Klemmenspannungen. Die Kirchhoffsche Schleifenregel gibt den Strom an.
Die Reihenschaltung erhöht zwar die zugeführte Spannung, erhöht aber auch den äquivalenten Innenwiderstand.
Die äquivalente Klemmenspannung kann für N in Reihe geschaltete Batterien verallgemeinert werden.
Wenn zwei Batterien mit identischer EMK parallel zu einem Lastwiderstand geschaltet werden, entspricht die Gesamt-EMK der EMK der einzelnen Batterien.
Unter Anwendung der Kirchhoffschen Sperrschichtregel am gemeinsamen Knoten, der Kirchhoffschen Schleifenregel für Schleife 1 und für Schleife 2 werden die Gleichungen gelöst, um den Laststrom über den Ersatzwiderstand zu bestimmen. Somit wird die Klemmenspannung erhalten.
Durch die Parallelschaltung wird der Innenwiderstand reduziert und es kann ein großer Strom erzeugt werden.
Der Ausdruck der äquivalenten Anschlussspannung kann für N Batterien parallel verallgemeinert werden.
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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.