Yes. I think you've almost got it.
If the voltage across the battery stays the same, then the SUM of the voltages across everything connected to the battery will always be that same total voltage.
Current is a separate concept and mechanism from voltage, but related. Voltage only gives the potential for current to flow, IF there is a conductive path.
If you connect a wire across the battery, a lot of current will flow, because the metal wire is a very low-value resistor, i.e. it's mostly just a good conductor.
If you change the wire so that it's NOT pure metal, making its resistance higher, it won't conduct as well and less current will flow. You have made its resistance higher.
If you insert a block of carbon in place of a small part of the wire, probably not nearly as much current could flow, because the carbon just isn't nearly as good at conducting electricity as the metal wire. The carbon is a "resistor". It resists letting current flow as well as it would in a metal wire.
Thinking only about resistors, imagine putting three different-valued resistors in series across the battery. The current will be determined by the total resistance, i.e. the sum of the three resistors' values. And that same current will flow through all three of them. I = V/(R1 + R2 + R3). There is only one path so the currents in every resistor and wire link in the whole path must be equal.
But the voltage that the current INDUCES across each resistor will be different, if the resistance values are different. Each one is just V = I * R, for R1, R2, and R3. So V1 = I * R1, V2 = I * R2, and V3 = I *R3.
Maybe THAT is the cause-and-effect mechanism you have been seeking to grok? A current through a resistor will INDUCE a proportional voltage across that resistor. But, also, a voltage across a resistor will induce a proportional current to flow through the resistor. Which one you think of as the cause and which one you think of as the effect can vary, depending on the context of the circuit, and whatever helps you to understand, at the time. But still, in every case, V = I * R, and I = V / R, and R = V / I .
Of course, the resistor voltages will also all sum to be equal to the battery voltage. V(battery) = V1 + V2 + V3. But that's redundant information, at this point. Once you know any TWO of the three, V, I, and R, you know the third, or, rather, it has already been determined by the physics of the circuit, which happens to be described by Ohm's Law in this case.
You can think of the voltage across each resistor as voltage "drop". But that's not really a very general way to look at it. It's better to realize that the sum of all of the voltages around any loop must be zero (since when you get all the way around you are back at the starting point and the voltage between a point and itself must be zero).
(Generalizing: )
That's called "Kirchoff's Voltage Law". Using that law, you can imagine the current in any loop to be in either direction and then write the loop equation by writing an expression for the sum of the voltages across the devices around the loop, in terms of that current, and setting their sum to zero.
If you have a bunch of interlocking circuit loops, you write an equation for each loop. Solving the resulting system of equations simultaneously gives you all of the voltages and currents, everywhere in the circuit.
There is also Kirchoff's Current Law, which simply states that the sum of all of the currents flowing into a single point must be zero. i.e. The current into a node equals the current out of that node. (A node is, say, a point where two or more wires connect to each other.)
So, for a complex-topology circuit, you can write a set of loop-voltage and/or node-current equations and solve them all simultaneously, to find all of the voltages and currents, everywhere in the circuit.
Cheers,
Tom
"Current does not follow the path of least resistance. It follows ALL paths, in inverse proportion to their resistances."
If the voltage across the battery stays the same, then the SUM of the voltages across everything connected to the battery will always be that same total voltage.
Current is a separate concept and mechanism from voltage, but related. Voltage only gives the potential for current to flow, IF there is a conductive path.
If you connect a wire across the battery, a lot of current will flow, because the metal wire is a very low-value resistor, i.e. it's mostly just a good conductor.
If you change the wire so that it's NOT pure metal, making its resistance higher, it won't conduct as well and less current will flow. You have made its resistance higher.
If you insert a block of carbon in place of a small part of the wire, probably not nearly as much current could flow, because the carbon just isn't nearly as good at conducting electricity as the metal wire. The carbon is a "resistor". It resists letting current flow as well as it would in a metal wire.
Thinking only about resistors, imagine putting three different-valued resistors in series across the battery. The current will be determined by the total resistance, i.e. the sum of the three resistors' values. And that same current will flow through all three of them. I = V/(R1 + R2 + R3). There is only one path so the currents in every resistor and wire link in the whole path must be equal.
But the voltage that the current INDUCES across each resistor will be different, if the resistance values are different. Each one is just V = I * R, for R1, R2, and R3. So V1 = I * R1, V2 = I * R2, and V3 = I *R3.
Maybe THAT is the cause-and-effect mechanism you have been seeking to grok? A current through a resistor will INDUCE a proportional voltage across that resistor. But, also, a voltage across a resistor will induce a proportional current to flow through the resistor. Which one you think of as the cause and which one you think of as the effect can vary, depending on the context of the circuit, and whatever helps you to understand, at the time. But still, in every case, V = I * R, and I = V / R, and R = V / I .
Of course, the resistor voltages will also all sum to be equal to the battery voltage. V(battery) = V1 + V2 + V3. But that's redundant information, at this point. Once you know any TWO of the three, V, I, and R, you know the third, or, rather, it has already been determined by the physics of the circuit, which happens to be described by Ohm's Law in this case.
You can think of the voltage across each resistor as voltage "drop". But that's not really a very general way to look at it. It's better to realize that the sum of all of the voltages around any loop must be zero (since when you get all the way around you are back at the starting point and the voltage between a point and itself must be zero).
(Generalizing: )
That's called "Kirchoff's Voltage Law". Using that law, you can imagine the current in any loop to be in either direction and then write the loop equation by writing an expression for the sum of the voltages across the devices around the loop, in terms of that current, and setting their sum to zero.
If you have a bunch of interlocking circuit loops, you write an equation for each loop. Solving the resulting system of equations simultaneously gives you all of the voltages and currents, everywhere in the circuit.
There is also Kirchoff's Current Law, which simply states that the sum of all of the currents flowing into a single point must be zero. i.e. The current into a node equals the current out of that node. (A node is, say, a point where two or more wires connect to each other.)
So, for a complex-topology circuit, you can write a set of loop-voltage and/or node-current equations and solve them all simultaneously, to find all of the voltages and currents, everywhere in the circuit.
Cheers,
Tom
"Current does not follow the path of least resistance. It follows ALL paths, in inverse proportion to their resistances."
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