A capacitor is a component used for storing electrical charge, and usually consists of two plates or sheets of conductor placed very close to (but not touching) each other. As the capacitor charges up, one of these conductors becomes positively charged while the other one becomes negatively charged.
When N capacitances are connected in series and a voltage V is applied across them, V = V1 + V2 + ... + VN = Q1/C1 + Q2/C2 + ... + QN/CN where Qi and Vi are the corresponding charge in and voltage across every individual capacitance Ci, respectively.
However, Q1 = Q2 = ... = QN, since each capacitor in the series experiences the same current or flow of charge. From earlier equations, Q/Ceff = Q/C1 + Q/C2 + ... + Q/CN. This equation may be simplified as follows: 1/Ceff = 1/C1 + 1/C2 + ... + 1/CN.
Thus, the reciprocal of the effective capacitance of N capacitors connected in series is equal to the sum of the reciprocals of their individual capacitances, i.e., 1/Ceff = 1/C1 + 1/C2 + ... + 1/CN.
When two or more capacitors are connected in parallel, the voltages across each of them are equal. However, the corresponding charge accumulated in each of them differs in accordance with the equation Q = CV. Thus, for a given circuit consisting of N capacitors connected in parallel and excited by a voltage V, V = Q1/C1 = Q2/C2 = ... = QN/CN, where Qi and Vi are the corresponding charge in and voltage across every individual capacitance Ci, respectively.
The total amount charge Q accumulated by all the capacitors is equal to the sum of the individual charges accumulated by the individual capacitances, or Q = Q1 + Q2 + ... + QN, which may be rewritten as CeffV = C1V + C2V + ... + CNV, since the voltage across all the capacitors is V. This equation may be simplified as follows: Ceff = C1 + C2 + ... + CN.
Thus, the effective capacitance of N capacitors connected in parallel is just the sum of their individual capacitances, i.e., Ceff = C1 + C2 + ... + CN.
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A capacitor is a component used for storing electrical charge, and usually consists of two plates or sheets of conductor placed very close to (but not touching) each other. As the capacitor charges up, one of these conductors becomes positively charged while the other one becomes negatively charged.
Capacitance (C) is defined as the ratio of the charge (Q) stored in a capacitor to the voltage (V) across the capacitor.
Mathematically, C = Q/V.
The unit of measurement for capacitance is the 'farad', F, which is defined as coulomb/volt.
The higher the capacitance of a capacitor, the greater is the charge it can store for a given voltage across it.
When N capacitances are connected in series and a voltage V is applied across them,
V = V1 + V2 + ... + VN = Q1/C1 + Q2/C2 + ... + QN/CN
where Qi and Vi are the corresponding charge in and voltage across every individual capacitance Ci, respectively.
However, Q1 = Q2 = ... = QN, since each capacitor in the series experiences the same current or flow of charge. From earlier equations, Q/Ceff = Q/C1 + Q/C2 + ... + Q/CN. This equation may be simplified as follows: 1/Ceff = 1/C1 + 1/C2 + ... + 1/CN.
Thus, the reciprocal of the effective capacitance of N capacitors connected in series is equal to the sum of the reciprocals of their individual capacitances, i.e., 1/Ceff = 1/C1 + 1/C2 + ... + 1/CN.
When two or more capacitors are connected in parallel, the voltages across each of them are equal. However, the corresponding charge accumulated in each of them differs in accordance with the equation Q = CV. Thus, for a given circuit consisting of N capacitors connected in parallel and excited by a voltage V,
V = Q1/C1 = Q2/C2 = ... = QN/CN,
where Qi and Vi are the corresponding charge in and voltage across every individual capacitance Ci, respectively.
The total amount charge Q accumulated by all the capacitors is equal to the sum of the individual charges accumulated by the individual capacitances, or
Q = Q1 + Q2 + ... + QN, which may be rewritten as
CeffV = C1V + C2V + ... + CNV,
since the voltage across all the capacitors is V. This equation may be simplified as follows: Ceff = C1 + C2 + ... + CN.
Thus, the effective capacitance of N capacitors connected in parallel is just the sum of their individual capacitances, i.e., Ceff = C1 + C2 + ... + CN.
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