25.3
Condensateurs en série et en parallèle
Plusieurs condensateurs connectés servent de composants électriques dans diverses applications. Ces multiples condensateurs se comportent comme un seu…
Les condensateurs peuvent être connectés en série ou en parallèle dans un circuit.
Considérons les condensateurs connectés en série à une batterie : la plaque connectée à la borne positive de la batterie développe une charge positive tandis que la plaque attachée à la borne négative est chargée négativement.
Une intensité égale de la charge est induite sur les autres plaques. Cependant, la différence de potentiel aux bornes de chaque condensateur varie en fonction du rapport entre la charge et sa capacité.
Si l’on considère les condensateurs comme un seul condensateur équivalent, la différence de potentiel aux bornes est égale à la somme des potentiels aux bornes de chaque condensateur.
Ainsi, l’inverse de la capacité équivalente est la somme des réciproques des capacités individuelles.
Maintenant, si les condensateurs sont connectés en parallèle, la différence de potentiel de chaque condensateur est égale à la tension de la batterie. Par conséquent, la charge varie en fonction du produit de la capacité des condensateurs individuels et de la différence de potentiel.
La charge totale du condensateur équivalent dans une connexion parallèle est la somme des charges des condensateurs individuels. Par conséquent, la capacité équivalente est additive.
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Q1: What happens to charge distribution when capacitors are connected in series?
In a series connection, each capacitor acquires an equal magnitude of charge Q. The plate connected to the battery's positive terminal develops a +Q charge, while the plate attached to the negative terminal is negatively charged at −Q. Charges are induced on the other plates so that the sum of charges on any pair of capacitor plates equals zero.
Q2: How does the potential difference vary across capacitors in a series circuit?
The potential drop on each capacitor in series varies as the ratio of the charge to its capacitance. The sum of potential drops across each capacitor equals the total battery voltage. Therefore, capacitors with lower capacitance experience larger potential differences than those with higher capacitance.
Q3: What is the formula for equivalent capacitance in a series configuration?
The reciprocal of equivalent capacitance in a series circuit equals the sum of reciprocals of individual capacitances: 1/Ceq = 1/C1 + 1/C2 + 1/C3. The resulting equivalent capacitance is always smaller than the smallest individual capacitance in the combination, reducing overall storage capacity.
Q4: Why does the voltage drop remain constant across capacitors in parallel?
In a parallel connection, the positive terminals of all capacitors connect to the battery's positive terminal, and negative terminals connect to the battery's negative terminal. This configuration ensures that the potential difference across each capacitor equals the battery voltage, remaining constant regardless of individual capacitance values.
Q5: How is the total charge calculated in a parallel capacitor network?
The total charge stored by a parallel network equals the sum of charges stored in each individual capacitor. Since charge varies as the product of capacitance and potential difference, and voltage is constant across all capacitors, higher capacitance values store proportionally more charge.
Q6: What is the equivalent capacitance formula for capacitors in parallel?
The equivalent capacitance in a parallel circuit equals the sum of all individual capacitances: Ceq = C1 + C2 + C3. This additive relationship means the parallel combination resembles a single equivalent capacitor with higher total capacitance than any individual component in the network.
Q7: How do series and parallel capacitor configurations differ in their capacitance outcomes?
Series configurations produce an equivalent capacitance smaller than the smallest individual capacitor, reducing total storage capacity. Parallel configurations produce an equivalent capacitance equal to the sum of individual capacitances, increasing total storage capacity. The choice between configurations depends on whether reduced or increased capacitance is desired for the application.