27.8
複数の電圧源
一般に、一部のデバイスに電力を供給するには、単一のバッテリーでは不十分です。 このような場合、バッテリーは直列または並列の 2 つの方法で組み合わせることができます。
直列では、1 つのバッテリーのプラス端子が別のバッテリーのマイナス端子に接続されます。 したがって、各バッテリーの電圧が加算されて正…
2つのバッテリーが負荷抵抗で直列に接続されている場合、全体の起電力は個々のバッテリーの起電力の合計になります。内部抵抗の合計は、個々の内部抵抗の合計です。各バッテリーには同じ電流が流れます。
端子電圧は、個々の端子電圧の合計です。キルヒホッフのループルールは電流を与えます。
直列接続により供給電圧は増加しますが、等価内部抵抗も増加します。
等価端子電圧は、直列のN電池について一般化できます。
同じ起電力を持つ2つのバッテリが負荷抵抗に並列に接続されている場合、合計起電力は個々のバッテリの電力と同じになります。
共通ノードにキルヒホッフの接合法則、ループ1にキルヒホッフのループ法則、およびループ2に適用すると、方程式が解かれ、等価抵抗を介した負荷電流が決定されます。これにより、端子電圧が得られる。
並列接続により内部抵抗が減少し、大きな電流を生成できます。
等価端子電圧の式は、N個のバッテリーを並列にした場合に一般化できます。
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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.