25.3
Capacitores em Série e em Paralelo
Múltiplos capacitores conectados servem como componentes elétricos em diversas aplicações. Esses múltiplos capacitores se comportam como um único capa…
Os capacitores podem ser conectados em configurações em série ou paralelas em um circuito.
Considere os capacitores conectados em série a uma bateria; a placa conectada ao terminal positivo da bateria desenvolve uma carga positiva enquanto a placa conectada ao terminal negativo é carregada negativamente.
Uma magnitude igual da carga é induzida nas outras placas. No entanto, a diferença de potencial em cada capacitor varia de acordo com a relação entre a carga e sua capacitância.
Considerando os capacitores como um único capacitor equivalente, a diferença de potencial entre ele é igual à soma dos potenciais em cada capacitor.
Assim, o recíproco da capacitância equivalente é a soma dos recíprocos das capacitâncias individuais.
Agora, se os capacitores estiverem conectados em paralelo, a diferença de potencial de cada capacitor será igual à tensão da bateria. Portanto, a carga varia conforme o produto da capacitância de capacitores individuais e a diferença de potencial.
A carga total do capacitor equivalente em uma conexão paralela é a soma das cargas dos capacitores individuais. Portanto, a capacitância equivalente é aditiva.
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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.