27.8
Sources de tension multiples
Généralement, une seule batterie n'est pas suffisante pour alimenter certains appareils. Dans de tels cas, les batteries peuvent être combinées de deu…
Lorsque deux batteries sont connectées en série avec une résistance de charge, la f.é.m. globale est la somme des f.é.m. des batteries individuelles. La résistance interne totale est la somme des résistances internes individuelles. Le même courant circule dans chaque batterie.
La tension aux bornes est la somme des tensions aux bornes individuelles. La règle de la boucle de Kirchhoff donne le courant.
Bien que la connexion en série augmente la tension fournie, elle augmente également la résistance interne équivalente.
La tension aux bornes équivalente peut être généralisée pour les batteries N en série.
Lorsque deux batteries avec des CEM identiques sont connectées en parallèle à une résistance de charge, la CEM totale est la même que les CEM des batteries individuelles.
En appliquant la règle de jonction de Kirchhoff au nœud commun, la règle de la boucle de Kirchhoff pour la boucle 1 et la boucle 2, les équations sont résolues pour déterminer le courant de charge via la résistance équivalente. Ainsi, la tension aux bornes est obtenue.
La connexion parallèle réduit la résistance interne et peut produire un courant important.
L’expression équivalente de la tension aux bornes peut être généralisée pour N batteries en parallèle.
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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.