- #1
bagasme
- 79
- 9
- TL;DR Summary
- Standard or Flipped One?
Hello,
As far as I know, the standard sign convention for Kirchhoff's law are:
from this homework forum. The problem image:
By standard sign convention, the equations are:
$$\begin{align}
I_1 + I_2 &= I_3 \nonumber \\
6 - 3I_1 - 3I_3 &=0 \nonumber \\
6 - 6I_2 - 3I_3 &=0 \nonumber
\end{align}$$
Solving the equation, we have ##I_1 = \frac 4 5 A, I_2 = \frac 2 5 A, I_3 = \frac 6 5 A##.
By flipped sign convention, the equations are:
$$\begin{align}
I_1 + I_2 &= I_3 \nonumber \\
-6 + 3I_1 - 3I_3 &= 0 \nonumber \\
-6 + 6I_2 + 3I_3 &= 0 \nonumber
\end{align}$$
Solving the equation, we have same solutions as above with standard convention.
I have questions:
As far as I know, the standard sign convention for Kirchhoff's law are:
- For resistor: the potential difference (voltage) is negative if the chosen loop direction is the same as chosen current direction through the resistor, positive otherwise.
- For battery: the voltage is positive if the chosen loop direction is from negative toward positive terminal, positive otherwise.
- For resistor: the voltage is positive if the chosen loop direction is the same as chosen current direction through the resistor, negative otherwise.
- For battery: the voltage is negative if the chosen loop direction is from negative toward positive terminal, positive otherwise.
from this homework forum. The problem image:
By standard sign convention, the equations are:
$$\begin{align}
I_1 + I_2 &= I_3 \nonumber \\
6 - 3I_1 - 3I_3 &=0 \nonumber \\
6 - 6I_2 - 3I_3 &=0 \nonumber
\end{align}$$
Solving the equation, we have ##I_1 = \frac 4 5 A, I_2 = \frac 2 5 A, I_3 = \frac 6 5 A##.
By flipped sign convention, the equations are:
$$\begin{align}
I_1 + I_2 &= I_3 \nonumber \\
-6 + 3I_1 - 3I_3 &= 0 \nonumber \\
-6 + 6I_2 + 3I_3 &= 0 \nonumber
\end{align}$$
Solving the equation, we have same solutions as above with standard convention.
I have questions:
- In what cases both sign conventions produce same solutions, and in what cases different solutions are produced?
- Which convention is right, the standard or the flipped one?