Currents can be added when they are flowing in the same direction and have the same magnitude. This is known as the principle of superposition, which states that the total current at any point in a circuit is equal to the algebraic sum of the individual currents at that point.
The mathematical formula for adding currents is I = I1 + I2 + I3 + ... + In, where I represents the total current and I1, I2, I3, etc. represent the individual currents.
No, currents with different directions cannot be added. In fact, when currents flow in opposite directions, they cancel each other out and the resulting current is equal to the difference between the two currents.
The ability to add currents is important in circuit analysis and design. It allows us to predict the behavior of complex circuits by breaking them down into simpler parts and then adding the currents to find the total current at a specific point.
There are a few limitations to adding currents. Firstly, the principle of superposition only applies to linear circuits, where the relationship between current and voltage is proportional. Additionally, this principle assumes that there are no interactions between the individual currents, which may not always be the case in more complex circuits.