Capacitors can be connected in or , each with unique properties. Series connections have lower , while connections have higher. Understanding these configurations is crucial for designing and analyzing electrical circuits.
Calculating equivalent in complex circuits involves identifying series and parallel combinations. By applying the appropriate formulas and working step-by-step, you can simplify even intricate networks to a single equivalent capacitance.
Capacitor Configurations and Equivalent Capacitance
Capacitance formulas for configurations
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Capacitors connected end-to-end with only one path for current flow (e.g., two capacitors connected positive-to-negative)
Equivalent capacitance (Ceq) is the reciprocal of the sum of reciprocals of individual capacitances
Formula for equivalent capacitance in series: Ceq1=C11+C21+...+Cn1
across each is different, but the on each capacitor is the same (e.g., 5V across C1 and 3V across C2, but both have 10 of charge)
The across each capacitor in series adds up to the total voltage applied
Capacitors connected with their terminals directly connected to each other (e.g., positive-to-positive and negative-to-negative)
Equivalent capacitance is the sum of individual capacitances
Formula for equivalent capacitance in parallel: Ceq=C1+C2+...+Cn
Voltage across each capacitor is the same, but the charge on each capacitor is different (e.g., 5V across both C1 and C2, but C1 has 10µC and C2 has 20µC of charge)
Series vs parallel capacitor connections
Series connection
Capacitors connected end-to-end forming a single path for current flow
Total voltage across the series combination is the sum of voltages across each capacitor (e.g., 5V across C1 and 3V across C2 results in 8V total)
Charge on each capacitor is the same
Equivalent capacitance is always less than the smallest individual capacitance (e.g., two 10 capacitors in series have an equivalent capacitance of 5µF)
Parallel connection
Capacitors connected with their terminals directly connected to each other
Voltage across each capacitor is the same and equal to the total voltage across the parallel combination
Total charge stored in the parallel combination is the sum of charges on each capacitor (e.g., 10µC on C1 and 20µC on C2 results in 30µC total)
Equivalent capacitance is always greater than the largest individual capacitance (e.g., two 10µF capacitors in parallel have an equivalent capacitance of 20µF)
Equivalent capacitance in combined circuits
Identify series and parallel combinations within the circuit
Calculate the equivalent capacitance for each series or parallel combination using the appropriate formula
For series combinations: Ceq1=C11+C21+...+Cn1
For parallel combinations: Ceq=C1+C2+...+Cn
Repeat the process, treating the equivalent capacitances as individual capacitors, until a single equivalent capacitance is obtained for the entire circuit (e.g., calculate equivalent capacitance for a series combination, then use that value in a parallel combination with another capacitor)
Remember that capacitors in series have the same charge, while capacitors in parallel have the same voltage across them
Capacitor Properties and Electric Field
Capacitance is a measure of a capacitor's ability to store
The between capacitor plates is responsible for storing energy
A material between capacitor plates can increase capacitance by reducing the electric field strength