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Resistance in parallel and in series
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When the resistors are connected in parallel, they are all exposed to the same potential difference which, by Ohm's law, generates different currents. The total current is the sum of the partial currents, so the total resistance is the inverse of the sum of the inverse of the individual resistances.
ID:(2121, 0)
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Equations
$ \Delta\varphi = \Delta\varphi_1 + \Delta\varphi_3 $
Dphi = Dphi_1 + Dphi_2
$ \Delta\varphi_1 = R_p I $
Dphi = R * I
$ \Delta\varphi_1 = R_1 I_1 $
Dphi = R * I
$ \Delta\varphi_1 = R_2 I_2 $
Dphi = R * I
$ \Delta\varphi_3 = R_3 I $
Dphi = R * I
$ \Delta\varphi = R_s I $
Dphi = R * I
$ I = I_1 + I_2 $
I = I_1 + I_2
$ R_s = R_p + R_3 $
R_s = R_1 + R_2
$\displaystyle\frac{1}{ R_p }=\displaystyle\frac{1}{ R_1 }+\displaystyle\frac{1}{ R_2 }$
1/ R_p =1/ R_1 + 1/ R_2
ID:(16023, 0)
Resistance in parallel (2)
Equation
The inverse of the resistance in Parallel ($R_p$) is equal to the sum of the inverses of the resistance 1 ($R_1$) and the resistance 2 ($R_2$). This relationship is expressed as:
| $\displaystyle\frac{1}{ R_p }=\displaystyle\frac{1}{ R_1 }+\displaystyle\frac{1}{ R_2 }$ |
ID:(16006, 0)
Series resistance (2)
Equation
In the case of two resistors connected in series, the resistance in Series ($R_s$) is equal to the sum of the resistance 1 ($R_1$) and the resistance 2 ($R_2$). This relationship is expressed as:
| $ R_s = R_p + R_3 $ |
| $ R_s = R_1 + R_2 $ |
None
ID:(16004, 0)
Sum of currents (2)
Equation
By the principle of conservation of electric charge, the current ($I$) is equal to the sum of the current 1 ($I_1$) and the current 2 ($I_2$). This relationship is expressed as:
| $ I = I_1 + I_2 $ |
ID:(16009, 0)
Sum of potential difference (2)
Equation
By the principle of energy conservation, the potential difference ($\Delta\varphi$) is equal to the sum of the difference of potential 1 ($\Delta\varphi_1$) and the difference of potential 2 ($\Delta\varphi_2$). This can be expressed through the following relationship:
| $ \Delta\varphi = \Delta\varphi_1 + \Delta\varphi_3 $ |
| $ \Delta\varphi = \Delta\varphi_1 + \Delta\varphi_2 $ |
ID:(16012, 0)
Ohm's law (1)
Equation
Traditional Ohm's law establishes a relationship between the potential difference ($\Delta\varphi$) and the current ($I$) through the resistance ($R$), using the following expression:
| $ \Delta\varphi_1 = R_p I $ |
| $ \Delta\varphi = R I $ |
None
ID:(3214, 1)
Ohm's law (2)
Equation
Traditional Ohm's law establishes a relationship between the potential difference ($\Delta\varphi$) and the current ($I$) through the resistance ($R$), using the following expression:
| $ \Delta\varphi_1 = R_1 I_1 $ |
| $ \Delta\varphi = R I $ |
None
ID:(3214, 2)
Ohm's law (3)
Equation
Traditional Ohm's law establishes a relationship between the potential difference ($\Delta\varphi$) and the current ($I$) through the resistance ($R$), using the following expression:
| $ \Delta\varphi_1 = R_2 I_2 $ |
| $ \Delta\varphi = R I $ |
None
ID:(3214, 3)
Ohm's law (4)
Equation
Traditional Ohm's law establishes a relationship between the potential difference ($\Delta\varphi$) and the current ($I$) through the resistance ($R$), using the following expression:
| $ \Delta\varphi_3 = R_3 I $ |
| $ \Delta\varphi = R I $ |
None
ID:(3214, 4)
Ohm's law (5)
Equation
Traditional Ohm's law establishes a relationship between the potential difference ($\Delta\varphi$) and the current ($I$) through the resistance ($R$), using the following expression:
| $ \Delta\varphi = R_s I $ |
| $ \Delta\varphi = R I $ |
None
ID:(3214, 5)