Capacitors in Series and Parallel: JEE Physics Mastery
Welcome to this module on understanding capacitors connected in series and parallel configurations. Mastering these concepts is crucial for excelling in competitive exams like JEE, particularly in the Electromagnetism section. We'll explore how these arrangements affect the overall capacitance, charge, and voltage.
Capacitors in Parallel
When capacitors are connected in parallel, their positive plates are connected together, and their negative plates are connected together. This means that the voltage across each capacitor is the same.
In parallel, total capacitance is the sum of individual capacitances.
When capacitors are connected in parallel, the total charge stored is the sum of charges on each capacitor. Since the voltage is the same across all, the equivalent capacitance is simply the sum of their individual capacitances: C_eq = C1 + C2 + C3 + ...
Consider capacitors C1, C2, and C3 connected in parallel across a voltage source V. The charge on each capacitor is Q1 = C1V, Q2 = C2V, and Q3 = C3V. The total charge stored is Q_total = Q1 + Q2 + Q3. If an equivalent capacitor C_eq were to store this total charge at the same voltage V, then Q_total = C_eqV. Substituting the individual charges, we get C_eqV = C1V + C2V + C3V. Dividing by V, we arrive at the formula for parallel capacitors: C_eq = C1 + C2 + C3 + ... This implies that the equivalent capacitance in a parallel combination is always greater than the largest individual capacitance.
Think of parallel capacitors like adding more lanes to a highway; it increases the overall capacity to store charge.
Capacitors in Series
In a series connection, capacitors are connected end-to-end, forming a single path for charge. The charge on each capacitor in a series combination is the same, but the voltage across them adds up.
When capacitors are connected in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances: 1/C_eq = 1/C1 + 1/C2 + 1/C3 + ... This means the equivalent capacitance is always less than the smallest individual capacitance. The voltage across each capacitor is inversely proportional to its capacitance (V = Q/C), so the smaller capacitor gets a larger share of the total voltage.
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In series, the reciprocal of total capacitance is the sum of reciprocals of individual capacitances.
When capacitors are connected in series, the charge on each capacitor is identical. The total voltage across the series combination is the sum of the voltages across each individual capacitor. The equivalent capacitance is found using the formula: 1/C_eq = 1/C1 + 1/C2 + 1/C3 + ...
Let's consider capacitors C1, C2, and C3 connected in series across a voltage source V. The charge Q stored on each capacitor is the same. The total voltage V is the sum of the voltages across each capacitor: V = V1 + V2 + V3. Since Q = C*V, we have V1 = Q/C1, V2 = Q/C2, and V3 = Q/C3. Substituting these into the voltage equation gives V = Q/C1 + Q/C2 + Q/C3. If an equivalent capacitor C_eq were connected to the same voltage V and stored the same charge Q, then V = Q/C_eq. Equating the two expressions for V, we get Q/C_eq = Q/C1 + Q/C2 + Q/C3. Dividing by Q (since Q is non-zero), we obtain the formula for series capacitors: 1/C_eq = 1/C1 + 1/C2 + 1/C3 + ... For two capacitors in series, this simplifies to C_eq = (C1 * C2) / (C1 + C2).
Connecting capacitors in series is like creating a bottleneck; it restricts the overall charge flow and reduces the effective capacitance.
C_eq = (C1 * C2) / (C1 + C2)
Greater
Summary of Key Differences
| Feature | Capacitors in Parallel | Capacitors in Series |
|---|---|---|
| Voltage | Same across all capacitors | Adds up; V_total = V1 + V2 + ... |
| Charge | Adds up; Q_total = Q1 + Q2 + ... | Same on all capacitors |
| Equivalent Capacitance Formula | C_eq = C1 + C2 + ... | 1/C_eq = 1/C1 + 1/C2 + ... |
| Effect on Capacitance | Increases total capacitance | Decreases total capacitance |
Learning Resources
Provides a clear, step-by-step explanation of how capacitors behave when connected in series and parallel, including derivations and examples.
An introductory video covering the basics of capacitance, followed by lessons on series and parallel combinations.
A blog post specifically tailored for JEE preparation, explaining series and parallel capacitor concepts with relevant formulas and solved examples.
Offers a comprehensive overview of capacitors in series and parallel, detailing the formulas and their applications with illustrative diagrams.
Explains the concept of equivalent capacitance for series combinations with a focus on problem-solving relevant to competitive exams.
A detailed explanation of series and parallel capacitor connections, including derivations and practice questions for JEE aspirants.
A university-level explanation of capacitor combinations, providing a solid theoretical foundation and mathematical derivations.
A video tutorial demonstrating how to solve problems involving capacitors connected in series and parallel, with clear explanations.
Provides concise notes and formulas for capacitors in series and parallel, ideal for quick revision before exams.
A forum discussion with expert answers and explanations regarding the behavior of capacitors in series and parallel configurations.