# Set up KVL in a simple circuit

For this circuit, is the correct KVL:

+10V-V1-V0-V2-(-10V)=0 ?

V0 between the resistors is an open-circuit voltage.

What is the voltage across R1? Is it V1=10V-V0?

And is V2=10V or V2=V0-(-10V)? simulate this circuit – Schematic created using CircuitLab

Thanks!

• Since your KVL looks good +10V-V1-V0-V2-(-10V) = 0 ; 10V-V1-V0-V2+10V = 0 And from there we can find V1 = 20V - V2 - V0 or V2 = 20V - V1 - V0
– G36
Apr 3 '17 at 15:44
• Your question will be easier to understand (for us and for you) if you draw the complete circuit, including the sources that produce the "+10 V" and "-10 V". Apr 3 '17 at 15:51
• Tip if V0 is open circuit what current is flowing in R1 and R2? What does ohms law tell you about the voltage drop across these trsistors? Apr 3 '17 at 16:13
• @WarrenHill V0 doesn't have any effect right? Ohm's law should be applied to R1 V1 and R2 V2. Isn't it?
– user105009
Apr 3 '17 at 17:14

The open circuit can be replaced by a resistor with infinite value (R3) If we assume that R3 indeed is infinite, R1 and R2 become so small in relation to R3, that we can disregard them. U = I*R, and since current is constant in a series connection, resistance will dictate the voltage distribution across resistors. Hence all voltage will fall across the infinite resistor R3. Now if we agree that R1 and R2 are so small we can disregard them, we are left with this circuit Now we just add all sources. VR3 = V1-V2 = 10 - (-10) = 10+10 = 20V

Hope this helps.

It doesn't look like V0 has an effect on the answer. It simply shifts the end points of the two resistors. They still collectively have 20V across them regardless of whether V0 is 0V or 1000V. In that case the current through R1 and R2 would be I = 20 / (R1 + R2). The voltage across R1 would be I * R1 = (20 * R1) / (R1 + R2).

If V0 is open circuit, then there is no current flowing and V0 = 20V. The voltage acrosss R1 is 0 and the voltage acrosss R2 is 0.

• Why really? I thought V1 produced a current through R1, I=V1/R1 and the same for V2, I2=V2/R2. Apr 3 '17 at 18:36
• The way I was taught is that the resistance of an open circuit is essentially infinity. That means that the current is V0 / infinity = 0. If there is no current, through R1, then there can be no voltage drop across it. Apr 3 '17 at 18:47