Current: Electronic and electrical things 'work' because electrons are flowing through them. This is current, abbreviation 'I', measured in amps. The more amps, the hotter, faster, louder, etc it will be. Talking of current is always relative to a single point in a circuit... the number of electrons passing that point. Current 'just happens' whenever you have a circuit.
Voltage: What makes the electrons move. Voltage is always a comparison between two points, but usually one of them is assumed to be the 'zero voltage' point chosen by the person who drew the circuit. Consider a single 1.5v 'battery'. (More properly called a cell.) If you attach your voltmeter to the two ends of the battery, it will read 1.5v. If you take a wire from the '+' end, to a light bulb, from there to second light bulb, and from that back to the '-' end of the battery and then get busy with your volt meter, you will discover the following: From + to - is still 1.5v (if your battery is fresh!) From '+' to the bit of wire between the bulbs is 0.75v. From the same bit of wire to '-': 0.75v again. Think of the electrons going around as being like climbing a mountain. The battery has whatever push it takes to get electrons all the way 'round. (You all the way to the top). If the path has obstacles, the push gets broken up as needed. Suppose your mountain has an ice cream seller at the half way point. To get there uses up half the push you have, the rest of the climb takes the other half. Voltage comes from cells, batteries, power supplies. Note that if you connect too little resistance (see next) to a given voltage source, the voltage it is meant to produce isn't supplied... and you may damgae things, too.
Resistance. Measured in ohms. Again, resistance is always a measurement of the resistance between two points. It is whatever makes it hard for electrons to go through the circuit. Without resistance, the amount of current from even one volt would be infinite. Anything electricity flows through will have some resistance, though the resistance of wire is too low to be important, generally speaking.
Easy when you know about the big three: If you have a fixed voltage, say 10 volts, then doubling the resistance in a circuit will half the current. Notice that the current is what it is, resulting from the facts of the voltage and resistance involved. To put it mathematically, the current will be the voltage divided by the current. E.g. With a voltage of 10v and a resistance of 100 ohms, the current will be 0.1 amp.
Remember that current is electrons flowing. Imagine your circuit as the Amazon River system. Where the part you are looking at has only one way for the water to get from A to B, the circuit is 'in series'. The light bulbs above were in series. Where the river splits into multiple channes (and rejoins later) the circuit is 'in parallel'. Some circuits, like the Amazon can be a mixture of series bits and parallel bits. If you zoom in on a small part, it can be series or parallel or a mixture.
When the two (or more) branches in a parallel circuit all have the same resistance, the current in each will be the same... a half (or third, etc) of the current 'upstream' of the branch. (The current after the branches rejoin will be the same as the current going in. You don't lose current, even if it may be split between paths.) If one path has twice the resistance of the other, it will have half the vurrent of the other.
Voltage is easy. You generally attach one probe to whatever part of the circuit the designer has called 'zero' volts, and then connect the other probe to the place you want to know about. Remeber that even though we talk about the voltage 'at such-and-such a point', implict is always the second part: 'compared to where we had the other probe.' Negligable amounts of electricity flow through the voltmeter, so you can measure voltages without distrubing the circuit.
Current is a little trickier. You have to 'cut a wire' (literally or effectively, e.g. by disconnecting one from come component of the circuit) and 'bridge the gap' with the ammeter. The ammeter has virtually no resistance, so be careful NOT, for instance, to connect it to the two ends of a battery: Some voltage + very little resistance = a high current, rapidly exhausted battery, and melted ammeter.
Resistance is a real pain. Generally, you have to remove the object of interest from the circuit and attache the ohmmeter probes to the two ends. It applies a voltage to the object, looks at the current which results, and decides from that what the resistance is. Note... transistors are 'non-ohmic' devides... you don't measure their 'resistance'. Neither would you put an ohmmeter on logic gates.
Forget watches. Forget music recording systems. (The words aren't misused in those cases, but the way they are used won't help you here.) In electronics, digital devices are those which, fundamentally, operate on an 'all or nothing' basis. They are 'on' or 'off', e.g. light bulbs (forgetting the possiblity of a diommer 'switch'.) Now... if you have a digital device with several parts, you can take a few 'on/offs' together and have a code with more than two possibilities... but the underlying components can only be 'on' or 'off'.
Analogue, on the other hand is the situation where you have gradations in between 'on' and 'off'. A radio is an analogue device because it can be off, soft, medium, loud, very loud, or outrageous.
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