25.4
Capacité équivalente
Plusieurs condensateurs peuvent être connectés dans un circuit en configuration série ou parallèle. Lorsque la combinaison de condensateurs est connec…
La capacité nette d’un réseau de condensateurs peut être calculée en trouvant les capacités équivalentes individuellement pour les combinaisons parallèle uniquement et série uniquement.
Considérons un réseau de condensateurs composé d’une combinaison en série et en parallèle de quatre condensateurs connectés à une batterie. Quelle est la charge à travers chaque condensateur ?
Comme les condensateurs 2 et 3 sont connectés en parallèle, la somme de leurs capacités donne la capacité équivalente.
Ainsi, le réseau à quatre condensateurs se réduit à trois condensateurs connectés en série.
Maintenant, la charge sur chaque condensateur a une amplitude égale, tandis que la différence de potentiel appliquée est égale à la somme de la tension aux bornes de chaque condensateur.
Étant donné que la tension est égale au rapport entre la charge et la capacité, la substitution des valeurs des capacités et de la tension appliquée donne la charge accumulée sur chaque condensateur en série.
La tension aux bornes des condensateurs 2 et 3 est égale et peut être obtenue à partir de la charge calculée.
Enfin, le produit des capacités individuelles et des valeurs de tension donne les charges sur les condensateurs 2 et 3.
Ainsi, les charges de tous les condensateurs du réseau sont estimées.
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Q1: How do you calculate equivalent capacitance for a mixed series and parallel network?
Identify and group capacitors connected in series separately from those in parallel. Calculate the equivalent capacitance for each group using the appropriate formula: sum reciprocals for series, sum values for parallel. Replace each group with its equivalent capacitor, then repeat until a single equivalent capacitance remains. This step-by-step reduction simplifies complex networks into manageable calculations.
Q2: Why is the charge magnitude the same across all capacitors in a series combination?
In a series circuit, capacitors are connected end-to-end with no branching paths. Charge cannot accumulate at intermediate points, so the same charge magnitude flows through each capacitor. The applied potential difference distributes across capacitors inversely proportional to their capacitances, but the charge stored on each remains equal.
Q3: What is the relationship between individual and equivalent capacitance in parallel circuits?
In a parallel combination, the equivalent capacitance equals the sum of all individual capacitances. This means the equivalent capacitance is always greater than any single capacitor in the network. Parallel capacitors share the same potential difference, allowing their charges to add together for increased total storage capacity.
Q4: How does equivalent capacitance in series compare to individual capacitor values?
The equivalent capacitance in a series circuit is always smaller than the smallest individual capacitance in the network. This occurs because the reciprocals of capacitances add together, reducing the overall ability to store charge. Series combinations are useful when lower capacitance values are needed or when voltage distribution is important.
Q5: What formula determines equivalent capacitance for capacitors connected in series?
For series capacitors, the reciprocal of equivalent capacitance equals the sum of reciprocals of individual capacitances: 1/Ceq = 1/C1 + 1/C2 + 1/C3. This relationship reflects how series connections restrict charge flow and reduce overall capacitance compared to parallel arrangements.
Q6: How do you find the charge on individual capacitors in a parallel network?
Calculate the charge on each parallel capacitor using Q = CV, where V is the common voltage across all parallel capacitors and C is the individual capacitance. Since all parallel capacitors experience the same potential difference, multiply each capacitance by this voltage to find its stored charge.
Q7: What happens to voltage distribution across capacitors in a series combination?
The total applied voltage distributes across series capacitors such that the sum of individual voltages equals the battery voltage. Each capacitor's voltage is inversely proportional to its capacitance: higher capacitance receives lower voltage. This voltage division is essential for protecting sensitive components in circuits.