Kirchoff's Voltage Law

Here is a powerful concept, that may seem a little trivial at first,
but its usefulness will grow if you stay with electronics stuff:

Put simply, Kirchoff's Voltage Law states that the sum of the voltages around a closed loop will always equal zero.

So first - some rules:

1. Assign a current, I, and stick with the direction
2. Assign polarities to the components in your circuit.
1. Voltage sources are "-" where the current goes in, and "+" where the current leaves.
2. Voltage consumers (resistors) are "+" where the current goes in, and "-" where the current leaves.
3. Write your equation, starting anywhere, and using the sign of the component where the current enters it.

So in the example above:

Since we know from Ohm's Law that Voltage = Current x Resistance:

So let's take a look at the result and see if it works:

So I = 1 amp

That makes the voltage drop across R₁  = 1 amp x 8 Ω = 8 volts

Similarly, the voltage drop across R₂ = 4 volts

So now we revisit the Kirchoff Voltage Loop and see that:

-12volts + 8volts +4volts = 0

One way this is useful is to consider the case of a blown fuse.

With the fuse blown, no current flows, but with the meter leads attached, a very small amount of current flows - indicated above by the grey arrows.

And we can use the Kirchoff Voltage Law to predict what the meter will read if the fuse is blown:

If  V_m  is the meter voltage, then the new loop becomes:

Now we find the current, I, in the circuit:

So the voltage drop across R1 = 12Ω x 1.2 micro amps (uA) = 14.4 micro volts (uV)

and the voltage drop across R2 = 8Ω x 1.2 uA = 9.6 uV

So now, without using the current to calculate the voltage across the meter resistance,

We can see that 12 volts - 14.4 micro volts - 9.6 micro volts -   V_m  = 0

And so  V_m = 12 volts - 24 micro volts, which = 11.999976 volts.

Since most meters won't display 8 digits, the meter will read 12 volts.

Conclusion:  If a fuse is blown in a series circuit, the voltage across the fuse will equal the source voltage.

Cheers for now.