The voltage across two components in series is zero. Is it possible that the voltages across the individual components aren't zero? Give an example.

When you're dealing with a series circuit, you're looking at a circuit where components are connected one after another, forming a single path for the current to flow. Imagine lining up batteries in a flashlight; the electricity has just one route from the first to the last component.

In a series circuit, the current remains constant throughout, which means that every component sees the same amount of current. A classic example of a series circuit is a string of old Christmas lights - when one bulb blows out, the entire string goes dark. This is because that broken bulb interrupts the single path of current flow.

It's also important to remember that in this type of circuit, the total resistance is the sum of individual resistances. This is due to the fact that the current has to pass through every resistor one by one, each adding its own share of resistance to the overall circuit.

Think of electrical voltage as the push that drives electric current through a circuit. You can compare it to water pressure in a hose; it's what propels water to move through. If voltage is high, you could say the push is strong.

Measured in volts, voltage is the potential difference between two points in a circuit. It's a bit like having two teams in a tug-of-war - the difference in strength between them would determine which way the rope moves. In an electrical circuit, one point is often the positive terminal of a power source with higher electrical potential, while the other is usually connected to the lower potential, like the negative terminal.

Keep in mind that voltage can exist across a component in a circuit without current if the circuit is open. It only starts to 'push' electrons and generate current when there's a closed, conducting path.

The behavior of resistors in series is essential to understanding circuits. You can think of resistors as narrow roads that slow down traffic - in this case, the 'traffic' is electric current. When you have multiple resistors in a series, it's akin to having several narrow roads in a row; the current has to squeeze through each one, which adds up to create more resistance.

Let's get into numbers. To find the total resistance in a series circuit, simply add up the resistance values of each individual resistor. So, if you have two resistors in series, one with a resistance of 3 ohms and another with 7 ohms, the total resistance would be \(3 \Omega + 7 \Omega = 10 \Omega\). This total resistance affects the voltage drop across each resistor, as described by Ohm's Law \(V = IR\), where \V\ is voltage, \I\ is current, and \R\ is resistance.

In practical terms, if you are using devices with resistors in series, it means they equally share the power source voltage based on their individual resistance values. This can be crucial for designing circuits that require specific voltages across certain components.

Fundamentals are key in electrical engineering, and a few basic principles set the foundation for analyzing and designing circuits. One of the bedrocks is Ohm's Law, which relates voltage (V), current (I), and resistance (R) in a simple formula \(V = IR\).

Another cornerstone is Kirchhoff's laws. We use Kirchhoff's Current Law (KCL) to understand that the total current entering a junction must equal the total current leaving it. Think of it as a roundabout in traffic; the amount of vehicles going in and out should be the same.

Kirchhoff's Voltage Law (KVL), on the other hand, tells us that the sum of all voltages around any closed loop in a circuit must equal zero. If you go on a hike and end up back at your starting point, no matter how many hills you climbed, your net altitude change is zero - that's the essence of KVL in terms of electrical potential.

These principles are integral to not only solving circuit problems but also in conceptualizing how circuits function - from powering the smallest electronic devices to running vast electrical grids.