Serial resistance: R_{total} = R_a + R _b

Serial voltage: V_{total} = V_a + V_b

Serial current: I_{total} = I_a = I_b

Parallel resistance: R_{total} = \frac{1}{1/R_a + 1/R_b}

Parallel voltage: V_{total} = V_a = V_b

Parallel current: I_{total} = I_a + I_b

Ohms law: V = I * R

Watt’s law: W = I * V

Simple, right? If you read everything so far and *understood* it, then you can stop reading, because you know everything you need to know about electronics.

Still here?

Ok, let’s explain what these things mean:

Let’s start with the three serial formulas. Let’s assume we have three points, P1, P2 and P3.

We hook up one component, called A between P1 and P2, and another component P2 and P3. We then hook up a battery between P1 and P3 to pass some current through these components.

Now we can measure the resistance between P1 and P2, which is the resistance of the A component, which we call R_a , and if we measure between P2 and P3, we get the resistance of the B component, which we call R_b . If we measure between P1 and P3, the resistance should be R_{total} which according to the formula above should be equal to R_a + R_b .

Thus, we can summarize the first formula as: **In a serial circuit, resistance adds.**

For the second formula, we’ll need to hook up a battery to P1 and P3. This will send some current through our circuit. We can then switch out multimeter to DC voltage measurements and measure the same three spots again. This will give us V_a, V_b and V_{total}, which also add.

**In a serial circuit, voltage adds.**

If we want to measure the *current* that goes through this circuit, we have to cut the circuit somewhere and insert the multimeter at that point. However, as we can see from the third formula; it doesn’t matter where we cut the circuit, because there is the same amount of current at every point in the circuit. This is only true for serial circuits though, as soon as their is a branch in the circuit somewhere, then each branch will have a different amount of current.

**In a serial circuit, current is the same everywhere**

Ok, so, what if we have our components hooked up in parallel?

Now we only need two points, P1 and P2, because both component A and B are hooked up to P1 and P2.

Now, we have to be careful when measuring the resistance of the individual components. We can’t do it while the components are connected to P1/P2, because then we always get R_{total} . No problem though, we can remove the components from the circuit and measure them separately, or we can just take the measurements we did before, it’s the same component, so it should have the same resistance.

Now, the formula for parallel resistance is a little more complicated, but it can actually be derived from the other rules in this post if you really want to. I’m not going to go into details, but I will make a few observations that might be helpful:

- R_{total} is always less than R_a and R_b
- If R_a = R_b , then R_{total} = R_a / 2

Now, if we hook up a battery again, and measure V_a, V_b and V_{total}, we’ll see that they are the same, which should be kind of obvious, because we are measuring *at the same place*. And we can’t remove the components and measure the voltage separately.

**In a parallel circuit, voltage is the same across all components.**

We can however measure current through each component individually. We would just have to cut the circuit and insert a multimeter at each individual component, and at the battery to measure the total. The total current should then be the sum of the current through each component. Just like if you had multiple rivers flowing into one larger river.

**In parallel circuit, current adds.**

Ok, so why does it behave like this?

Well, the answer is basically Ohm’s law: V = I * R .

This law is *universal* and applies to all components, including wires, batteries and you.

One of the most useful aspects of this law is that if there is a resistor with a known value somewhere in a circuit, then we can measure the voltage across it and then we can calculate the current that is flowing through that resistor as I = V / R . This is in fact how a multimeter measures current. It has a small known resistor internally which it measures the voltage over. Since current is the same in all components hooked up in serial, we also know how much current is flowing everywhere else in the circuit.

Finally we have Watt’s law, which specifies how much *Power* a component is using: W = V * I .

Since Ohm’s law says that V = I * R , Watt’s law can also be written as W = I^2 * R .

Watt’s law is useful when estimating if a wire is thick enough. You just have to look up the resistance of the wire, and estimate how much current will go through it. Then you will know how many watts of power will be lost in the wire. Remember a 4-watt night light gets hot, so you probably don’t want to loose many watts of power in a wire.

Now go use it, practice makes perfect.