# AreKirchoff's laws of Current and Voltage interchangeable?

1. Mar 16, 2015

### C. Long

Specifically the equations you get when you examine the loops in a circuit.

2. Mar 16, 2015

### axmls

I'm not 100% sure what you're asking here. If you're wondering whether they're both valid fo whatever circuit you come across, then yes, they are. The difference is that the application of kirchoff's voltage law (using loop equations) usually yields currents whereas you get voltages from Kirchoff's current law (when applied to get nodal equations).

Otherwise, kirchoff's current law is basically a statement that current is preserved (it isn't created or destroyed), and Kirchoff's voltage law says that if you walk around the planet (a loop) and end up at the same spot, you're at the exact same elevation (voltage) as when you started.

So, if that's what you're asking, then they're not really "interchangeable". They're two different important laws.

3. Mar 16, 2015

### C. Long

You get currents from the voltage law and voltages from the current law?

4. Mar 16, 2015

### axmls

Yes. The laws in their stated forms aren't very mathematically useful. So, for instance, if you want to write Kirchoff's voltage law around a single loop, instead of writing $V_1 + V_1 + V_s = 0$, you could write $i R_1 + i R_2 + V_s = 0$ (this example is a single loop circuit, so there's only one current and it's through all the elements), and we know the resistances and the source voltage, so we can find a current, and that's from Kirchoff's voltage law.

5. Mar 16, 2015

### C. Long

Alright I think I see. I'm a little confused on the direction across batteries and resistors in terms of if the term is positive or negative. Our professor seems to flip flop; sometimes if the current is going neg to pos across the battery it's a positive voltage and other times it's a negative voltage.

Last edited: Mar 16, 2015
6. Mar 16, 2015

### axmls

Well, in passive convention, you assume a direction of the current, then every time you come across a resistor, you have the current entering the + voltage and leaving the - voltage. Whether you choose that to be positive or negative in your loop equation is irrelevant, but make sure that if you pass a voltage going from - to +, you use the opposite sign on that one.

7. Mar 16, 2015

### gleem

It is the usual convention that when going with the current from a high potential to a low ie. + to - as you would in a resistor that the voltage drop is taken as positive because work was done on the current. But when you from - to + as in a battery you must do work to get to the higher potential land this voltage drop is take as negative. So in a simple circuit in which a resistor is connected to a battery Kirchhoff's voltage law say the sum of the voltage drops around a loop must sum to zero i.e, Vr + Vb =0. So since the voltage drop across the battery and the resistor is the same say V then Kirchhoff's law is V+ (-V) = 0 of course which it obviously is. So when going with the current across a resistor, capacitor or inductor take the voltage drop as positive. When going against the current take these voltage drops as negative. But with a battery do just the opposite. And remember to write Kirchhoff's law in this form ∑ V = 0 around a loop when substituting in for the voltage drops

For Kirchhoff's current law ∑I = 0 for currents entering and leaving a node or junction you can take currents entering as positive and leaving as negative. . Remember the current stays in the same direction through a series connected branch.

Choose your currents first then determine the voltage drops. Usually start a the principle power source + terminal and proceed to the first node and continue through the circuit until you reach the - terminal of the principle power source combining and defining current directions in a consistent manner. Keep in mind that the current leaving the battery is the same as entering it.

8. Mar 16, 2015

### C. Long

Hey thanks guys I think I understand this now.