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I am having a problem with calculating the amount of current flowing through a branch, after deriving potential of its nodes using the Node Voltage Method.

I understand how to calculate voltage drop on a resistor and the voltage of an ideal voltage source as well:

The branch I am having problems with is sketched below:

The current I2 should be equal to I2 = U02/R2 = (E2-V2)/R2,$$I_2 = \frac{U_{02}}{R_2} = \frac{(E_2-V_2)}{R_2}$$ but I do not understand why this would be the case.

In the expression I2 = U02/R2$$I_2 = \frac{U_{02}}{R_2}$$ I tried to calculate the voltage U02 the way I thought was correct:

U02 = U0A + UA2 = -E2 + I2R2 ,$$U_{02} = U_{0A} + U_{A2} = -E_2 + I_2R_2$$ substituting in the previous equation:
I2 = (-E2 + I2R2) / R2$$I_2 =\frac{(-E_2 + I_2R_2)}{R_2}$$

If we multiply this with R2 we will get:
I2R2 = -E2 + I2R2$$I_2R_2 = -E_2 + I_2R_2$$
-E2 = 0$$-E_2 = 0$$ ???

and if we don't substitute anything, but rather continue with the expression for U02 we get:

U02 = U0A + UA2 = -E2 + I2R2$$U_{02} = U_{0A} + U_{A2} = -E_2 + I_2R_2$$
I2 = (U02 + E2)/R2$$I_2 = \frac{U_{02}+E_2}{R_2}$$, which would bring us to the suggested solution if it was true that:

U02 = V0 - V2 = -V2$$U_{02} = V_0 - V_2 = -V_2$$

which shouldn't be the case, since the voltage between 0 and 2 isn't determined only by potential difference between the nodes, but also the voltage generator that contributes as well.

I do not understand this at all and I feel like everything I've learned so far is not valid anymore. Things are literally making no sense. Where did I go wrong?

EDIT: To rephrase and recap: How to calculate the current I2 (second sketch) if values R2, E2 and V2 are known (V0 = 0) ?

I am having a problem with calculating the amount of current flowing through a branch, after deriving potential of its nodes using the Node Voltage Method.

I understand how to calculate voltage drop on a resistor and the voltage of an ideal voltage source as well:

The branch I am having problems with is sketched below:

The current I2 should be equal to I2 = U02/R2 = (E2-V2)/R2, but I do not understand why this would be the case.

In the expression I2 = U02/R2 I tried to calculate the voltage U02 the way I thought was correct:

U02 = U0A + UA2 = -E2 + I2R2 , substituting in the previous equation:
I2 = (-E2 + I2R2) / R2

If we multiply this with R2 we will get:
I2R2 = -E2 + I2R2
-E2 = 0 ???

and if we don't substitute anything, but rather continue with the expression for U02 we get:

U02 = U0A + UA2 = -E2 + I2R2
I2 = (U02 + E2)/R2, which would bring us to the suggested solution if it was true that:

U02 = V0 - V2 = -V2

which shouldn't be the case, since the voltage between 0 and 2 isn't determined only by potential difference between the nodes, but also the voltage generator that contributes as well.

I do not understand this at all and I feel like everything I've learned so far is not valid anymore. Things are literally making no sense. Where did I go wrong?

EDIT: To rephrase and recap: How to calculate the current I2 (second sketch) if values R2, E2 and V2 are known (V0 = 0) ?

I am having a problem with calculating the amount of current flowing through a branch, after deriving potential of its nodes using the Node Voltage Method.

I understand how to calculate voltage drop on a resistor and the voltage of an ideal voltage source as well:

The branch I am having problems with is sketched below:

The current I2 should be equal to $$I_2 = \frac{U_{02}}{R_2} = \frac{(E_2-V_2)}{R_2}$$ but I do not understand why this would be the case.

In the expression $$I_2 = \frac{U_{02}}{R_2}$$ I tried to calculate the voltage U02 the way I thought was correct:

$$U_{02} = U_{0A} + U_{A2} = -E_2 + I_2R_2$$ substituting in the previous equation:
$$I_2 =\frac{(-E_2 + I_2R_2)}{R_2}$$

If we multiply this with R2 we will get:
$$I_2R_2 = -E_2 + I_2R_2$$
$$-E_2 = 0$$ ???

and if we don't substitute anything, but rather continue with the expression for U02 we get:

$$U_{02} = U_{0A} + U_{A2} = -E_2 + I_2R_2$$
$$I_2 = \frac{U_{02}+E_2}{R_2}$$, which would bring us to the suggested solution if it was true that:

$$U_{02} = V_0 - V_2 = -V_2$$

which shouldn't be the case, since the voltage between 0 and 2 isn't determined only by potential difference between the nodes, but also the voltage generator that contributes as well.

I do not understand this at all and I feel like everything I've learned so far is not valid anymore. Things are literally making no sense. Where did I go wrong?

EDIT: To rephrase and recap: How to calculate the current I2 (second sketch) if values R2, E2 and V2 are known (V0 = 0) ?

2 added 125 characters in body

I am having a problem with calculating the amount of current flowing through a branch, after deriving potential of its nodes using the Node Voltage Method.

I understand how to calculate voltage drop on a resistor and the voltage of an ideal voltage source as well:

The branch I am having problems with is sketched below:

The current I2 should be equal to I2 = U02/R2 = (E2-V2)/R2, but I do not understand why this would be the case.

In the expression I2 = U02/R2 I tried to calculate the voltage U02 the way I thought was correct:

U02 = U0A + UA2 = -E2 + I2R2 , substituting in the previous equation:
I2 = (-E2 + I2R2) / R2

If we multiply this with R2 we will get:
I2R2 = -E2 + I2R2
-E2 = 0 ???

and if we don't substitute anything, but rather continue with the expression for U02 we get:

U02 = U0A + UA2 = -E2 + I2R2
I2 = (U02 + E2)/R2, which would bring us to the suggested solution if it was true that:

U02 = V0 - V2 = -V2

which shouldn't be the case, since the voltage between 0 and 2 isn't determined only by potential difference between the nodes, but also the voltage generator that contributes as well.

I do not understand this at all and I feel like everything I've learned so far is not valid anymore. Things are literally making no sense. Where did I go wrong?

EDIT: To rephrase and recap: How to calculate the current I2 (second sketch) if values R2, E2 and V2 are known (V0 = 0) ?

I am having a problem with calculating the amount of current flowing through a branch, after deriving potential of its nodes using the Node Voltage Method.

I understand how to calculate voltage drop on a resistor and the voltage of an ideal voltage source as well:

The branch I am having problems with is sketched below:

The current I2 should be equal to I2 = U02/R2 = (E2-V2)/R2, but I do not understand why this would be the case.

In the expression I2 = U02/R2 I tried to calculate the voltage U02 the way I thought was correct:

U02 = U0A + UA2 = -E2 + I2R2 , substituting in the previous equation:
I2 = (-E2 + I2R2) / R2

If we multiply this with R2 we will get:
I2R2 = -E2 + I2R2
-E2 = 0 ???

and if we don't substitute anything, but rather continue with the expression for U02 we get:

U02 = U0A + UA2 = -E2 + I2R2
I2 = (U02 + E2)/R2, which would bring us to the suggested solution if it was true that:

U02 = V0 - V2 = -V2

which shouldn't be the case, since the voltage between 0 and 2 isn't determined only by potential difference between the nodes, but also the voltage generator that contributes as well.

I do not understand this at all and I feel like everything I've learned so far is not valid anymore. Things are literally making no sense. Where did I go wrong?

I am having a problem with calculating the amount of current flowing through a branch, after deriving potential of its nodes using the Node Voltage Method.

I understand how to calculate voltage drop on a resistor and the voltage of an ideal voltage source as well:

The branch I am having problems with is sketched below:

The current I2 should be equal to I2 = U02/R2 = (E2-V2)/R2, but I do not understand why this would be the case.

In the expression I2 = U02/R2 I tried to calculate the voltage U02 the way I thought was correct:

U02 = U0A + UA2 = -E2 + I2R2 , substituting in the previous equation:
I2 = (-E2 + I2R2) / R2

If we multiply this with R2 we will get:
I2R2 = -E2 + I2R2
-E2 = 0 ???

and if we don't substitute anything, but rather continue with the expression for U02 we get:

U02 = U0A + UA2 = -E2 + I2R2
I2 = (U02 + E2)/R2, which would bring us to the suggested solution if it was true that:

U02 = V0 - V2 = -V2

which shouldn't be the case, since the voltage between 0 and 2 isn't determined only by potential difference between the nodes, but also the voltage generator that contributes as well.

I do not understand this at all and I feel like everything I've learned so far is not valid anymore. Things are literally making no sense. Where did I go wrong?

EDIT: To rephrase and recap: How to calculate the current I2 (second sketch) if values R2, E2 and V2 are known (V0 = 0) ?

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# Voltage drop of a non-ideal voltage source

I am having a problem with calculating the amount of current flowing through a branch, after deriving potential of its nodes using the Node Voltage Method.

I understand how to calculate voltage drop on a resistor and the voltage of an ideal voltage source as well:

The branch I am having problems with is sketched below:

The current I2 should be equal to I2 = U02/R2 = (E2-V2)/R2, but I do not understand why this would be the case.

In the expression I2 = U02/R2 I tried to calculate the voltage U02 the way I thought was correct:

U02 = U0A + UA2 = -E2 + I2R2 , substituting in the previous equation:
I2 = (-E2 + I2R2) / R2

If we multiply this with R2 we will get:
I2R2 = -E2 + I2R2
-E2 = 0 ???

and if we don't substitute anything, but rather continue with the expression for U02 we get:

U02 = U0A + UA2 = -E2 + I2R2
I2 = (U02 + E2)/R2, which would bring us to the suggested solution if it was true that:

U02 = V0 - V2 = -V2

which shouldn't be the case, since the voltage between 0 and 2 isn't determined only by potential difference between the nodes, but also the voltage generator that contributes as well.

I do not understand this at all and I feel like everything I've learned so far is not valid anymore. Things are literally making no sense. Where did I go wrong?