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Series capacities (3)
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In the case of series capacitance, the applied potential difference generates the same load on all plates, alternating only the sign of these. With this, each capacitance is under a different potential difference whose sum is equal to the potential difference applied. Since the potential differences are equal to the load divided by the capacitance, the inverse of the total capacitance is equal to the sum of the inverses of each capacitance.
ID:(2124, 0)
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$ \Delta\varphi = \Delta\varphi_1 + \Delta\varphi_2 + \Delta\varphi_3 $
Dphi = Dphi_1 + Dphi_2 + Dphi_3
$ \Delta\varphi =\displaystyle\frac{ Q }{ C_s }$
Dphi = Q / C
$ \Delta\varphi_1 =\displaystyle\frac{ Q }{ C_1 }$
Dphi = Q / C
$ \Delta\varphi_2 =\displaystyle\frac{ Q }{ C_2 }$
Dphi = Q / C
$ \Delta\varphi_3 =\displaystyle\frac{ Q }{ C_3 }$
Dphi = Q / C
$\displaystyle\frac{1}{ C_s }=\displaystyle\frac{1}{ C_1 }+\displaystyle\frac{1}{ C_2 }+\displaystyle\frac{1}{ C_3 }$
1/ C_s =1/ C_1 +1/ C_2 +1/ C_3
ID:(16026, 0)
Sum of series capacities (3)
Equation
The inverse of the sum capacity in serie ($C_s$) is calculated as the sum of the inverses of the capacity 1 ($C_1$), the capacity 2 ($C_2$) and the capacity 3 ($C_3$), according to the following relationship:
| $\displaystyle\frac{1}{ C_s }=\displaystyle\frac{1}{ C_1 }+\displaystyle\frac{1}{ C_2 }+\displaystyle\frac{1}{ C_3 }$ |
ID:(3870, 0)
Sum of potential difference (3)
Equation
By the principle of energy conservation, the potential difference ($\Delta\varphi$) is equal to the sum of the difference of potential 1 ($\Delta\varphi_1$), the difference of potential 2 ($\Delta\varphi_2$) and the difference of potential 3 ($\Delta\varphi_3$). This can be expressed through the following relationship:
| $ \Delta\varphi = \Delta\varphi_1 + \Delta\varphi_2 + \Delta\varphi_3 $ |
ID:(16013, 0)
Equation of a capacitor (1)
Equation
The potential difference ($\Delta\varphi$) generates the charge in the capacitor, inducing the charge ($Q$) on each side (with opposite signs), depending on the capacitor capacity ($C$), according to the following relationship:
| $ \Delta\varphi =\displaystyle\frac{ Q }{ C_s }$ |
| $ \Delta\varphi =\displaystyle\frac{ Q }{ C }$ |
ID:(3864, 1)
Equation of a capacitor (2)
Equation
The potential difference ($\Delta\varphi$) generates the charge in the capacitor, inducing the charge ($Q$) on each side (with opposite signs), depending on the capacitor capacity ($C$), according to the following relationship:
| $ \Delta\varphi_1 =\displaystyle\frac{ Q }{ C_1 }$ |
| $ \Delta\varphi =\displaystyle\frac{ Q }{ C }$ |
ID:(3864, 2)
Equation of a capacitor (3)
Equation
The potential difference ($\Delta\varphi$) generates the charge in the capacitor, inducing the charge ($Q$) on each side (with opposite signs), depending on the capacitor capacity ($C$), according to the following relationship:
| $ \Delta\varphi_2 =\displaystyle\frac{ Q }{ C_2 }$ |
| $ \Delta\varphi =\displaystyle\frac{ Q }{ C }$ |
ID:(3864, 3)
Equation of a capacitor (4)
Equation
The potential difference ($\Delta\varphi$) generates the charge in the capacitor, inducing the charge ($Q$) on each side (with opposite signs), depending on the capacitor capacity ($C$), according to the following relationship:
| $ \Delta\varphi_3 =\displaystyle\frac{ Q }{ C_3 }$ |
| $ \Delta\varphi =\displaystyle\frac{ Q }{ C }$ |
ID:(3864, 4)