Why does voltage drop in a series circuit but current stays the same?

Question

my basic understanding of electricity is as follows:

Voltage is the difference between the electric field strength of 2 points and how much work can be done by a charged particle as it is moved by those fields between those 2 points.

Current is the flow of charged particles and the consequence of voltage. There can be no current without voltage although there can be voltage without current.

Resistance is a measure of how much a material inhibits current.

The relationship between these three is expressed in an equation:

V = I x R

The problem I have is that when I apply this understanding to a series circuit, I struggle to wrap my head around how current and resistance can remain constant throughout the circuit but voltage varies? Shouldn't the current drop with the voltage? There are other people who have asked similar question but I could not really understand the answers so please keep it simple for me. Thank you.

Answer 1

I struggle to wrap my head around how current and resistance can remain constant throughout the [series] circuit but voltage varies? Shouldn't the current drop with the voltage?

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. Two 2 kΩ loads on a 10 V supply.

1. First thing: for a resistor, \$ I_{IN} = I_{OUT} \$. Otherwise mobile charges would pile up somewhere inside the component and this doesn't happen.
2. As a result of 1, current in a series circuit is the same throughout. In Figure 1 \$ I_{R1} = I_{R2} \$ and \$ I_{R3} = I_{R4} = I_{R5} \$.
3. Voltages is measured between two points. It is common to measure with respect to an arbitrary ground (battery negative in Figure 1) but can also be measured between any two points. VM3 shows the voltage at the top of R1 with respect to ground while VM1 shows the voltage between the terminals of R1.
4. The circuit consisting of R3, 4 and 5 has the same overall resistance but notice the way the voltage is divided in proportion to the value of the resistors.

Figure 2. See my answer to Intuitive interpretation of negative voltage for more on voltage references. Image original by @Transistor.

Answer 2

Understanding voltage will clear your confusion as to why voltage drops in series circuits and currents stays the same. Hence I will try to explain to voltage (electric potential difference) with a gravitational field analogy here before answering the question.

Explanation, pictures used are all belong to Physicsclassroom.com website.

Electric potential difference as voltage:

When this principle is logically extended to the movement of charge within an electric field, the relationship between work, energy and the direction that a charge moves becomes more obvious.

**Principle:** The natural direction of motion of an object is from high energy to low 
energy; but work must be done to move the object against nature. On the other hand, 
work would not be required to move an object from a high potential energy location to 
a low potential energy location. 

Two like charged objects repel and two oppositely charged objects attract each other. Here Source charge is represented by bigger circle and test charge by smaller circle and electric filed direction is shown by E vector in red.

When an object is moved against the electric field it gains some amount of energy which is defined as the electric potential energy. It depends on:
• Electric charge
• Distance from source location within the electric field.

Now we want a quantity that is not dependent on electric charge because when potential energy depends on charge we cannot define high potential and low potential locations.

**Suppose:**  1 Coulomb of charge at 1 unit of distance has 10 Joules of PE

              2 Coulombs of charge at 1 unit of distance has 20 Joules of PE

              1 Coulomb of charge at 2 units of distance also has 20 Joules of PE

Hence Electric Potential is defined.

Electric Potential:

• Electric potential is the potential energy per charge.

• While electric potential energy has a dependency upon the charge of the object experiencing the electric field, electric potential is purely location dependent.

• The concept of electric potential is used to express the effect of an electric field of a source in terms of the location within the electric field.

• A test charge with twice the quantity of charge would possess twice the potential energy at a given location; yet its electric potential at that location would be the same as any other test charge.

Electric Potential Difference OR Voltage:

• Consider the task of moving a positive test charge within a uniform electric field from location A to location B as shown in the diagram.

• In moving the charge against the electric field from location A to location B, work will have to be done on the charge by an external force.

• The work done on the charge changes its potential energy to a higher value; and the amount of work that is done is equal to the change in the potential energy.

• As a result of this change in potential energy, there is also a difference in electric potential between locations A and B.

• This difference in electric potential is represented by the symbol ΔV and is formally referred to as the electric potential difference.

• By definition, the electric potential difference is the difference in electric potential (V) between the final and the initial location when work is done upon a charge to change its potential energy.

• Because electric potential difference is expressed in units of volts, it is sometimes referred to as the voltage.

Current:

• Current has to do with the number of coulombs of charge that pass a point in the circuit per unit of time.

• A high current is a result of several coulombs of charge crossing over a cross section of a wire on a circuit.

• Current does not have to do with how far charges move in a second but rather with how many charges pass through a cross section of wire on a circuit.

What happens in a circuit?

1. Electric circuits are all about energy not about charge.
2. The charge is simply the medium which moves the energy from location to location.
3. Inside the battery it supplies the energy (this is the external energy needed to do work to move charge against the field and gain potential energy) needed to move a charge from a low potential to high potential.
4. Once a voltage and closed conducting path is established, charges naturally move from high potential location to low potential locations and lose their potential energy.
5. As charges move through loads (resistance etc), they transfer some of their potential energy to load and potential energy is converted to other form of energies (heat, light in case of a bulb etc) and hence loss in potential energy.
6. Each loss in potential energy is referred to as voltage drop.
7. Remember conservation of energy principle, whatever energy is gained by charges can only be lost by them. Hence total loss of electric potential of a single charge is equal to the gain in electric potential that it experiences in battery.

What happens in series circuit?

In series circuit connection, charges have only single path to move. Hence current is same everywhere in the circuit. As charges moves they transfer their potential energy to load and lose their potential energy hence voltage drops.

Answer 3

my basic understanding of electricity is as follows:

Voltage is the difference between the electric field strength of 2 points ...

It's the difference in electrical potential of 2 points. A field exists between 2 points if they're at different potentials

... and how much work can be done by a charged particle as it is moved by those fields between those 2 points.

moved by the field between the two points

Current is the flow of charged particles ...

The movement of charge. It's usually particles, though there's also 'displacement charge' between the plates of a capacitor that's due to polarisation of a material or of the vacuum

... and the consequence of voltage.

I don't like causation arguments, they can confuse people. Depending on how you set up an experiment, it can look like you're applying a voltage to some component and then a current flows. However, another experiment can look like you send a current through a component and create a voltage across it, for instance turning off the supply to a solenoid, and watching what happens at the catch diode.

There can be no current without voltage although there can be voltage without current.

That's just because we live in a world with imperfect conductors like copper, and very very good insulators like most plastics. If we had superconducting wires, and lived underwater (as highly evolved dolphins let's say) rather than in air, without access to plastics, then we'd put that the other way round. Current can flow without voltage in a superconductor, and any voltage difference between two points would result in the flow of current. So it's just an accident of the materials that are around us, not anything fundamental about electricity.

Resistance is a measure of how much a material inhibits current.

That's sufficiently vague that I'm not going to say it's incorrect, but don't try to read too much meaning into it or draw conclusions from it.

The relationship between these three is expressed in an equation:

V = I x R

Yes. However, we need to be careful that we measure V and I at the correct points, the relevant V is the voltage difference between the terminals of the component. We also need to know that resistance is not necessarily constant, or even linear. For metals, it is mostly both, and there exist metal alloys where it can be very constant with temperature indeed. 'Resistors' are generally made out of alloys like this.

The problem I have is that when I apply this understanding to a series circuit, I struggle to wrap my head around how current and resistance can remain constant throughout the circuit but voltage varies? Shouldn't the current drop with the voltage? There are other people who have asked similar question but I could not really understand the answers so please keep it simple for me. Thank you

Transistor's answer has a good diagram that I won't repeat here. Go back to my comment on V=IR, you need to choose V and I carefully, at the terminals of the same component. For each component in a series string of resistors, you must take the voltage difference across the ends of each component to use with I and R, not the voltage difference between a component terminal and some other reference like ground, which is changing as you go along a series string of components.

Answer 4

answer does not fit in comments hence posting a new answer.

Electric current is the rate of flow of charge caused by potential difference (voltage).

Flow of charge – means electrons (or holes) must move. Here electrons will move under external force which is supplied by electric field.

Hence understanding how the electric field changes inside circuit will help us understand why current is constant in series circuit.

We will recollect some points which will be very helpful in our analysis now:

I have provided explanation on why the below points are true at the end of the answer. You can check if you would like to refresh your memory

Electric field:

1. Electric field is a non-contact force. Unbalanced forces causes objects to accelerate in the direction of unbalanced force and a balance of force causes objects to remain at equilibrium. [Equilibrium and steady state are different]

2. Coulombs law states that the electrical force between two charged objects is a. Directly proportional to the product of the quantity of charges on the objects and b. Inversely proportional to the square of the separation distance between the two objects

      c.   F = [K (Q1)(Q2)]/d2
   
      d.   Electric field strength E = (K (Q1))/d2………F = E (Q2)
   

Surface Charge:

1. If conductor has acquired an excess charge, the excess charge quickly distributes only over the surface of conductor and not anywhere. Any excess charge will reside on the surface of the conductor.

Drift Speed:

1. The average speed of an electron in start–stop motion (due to collisions with atomic core) is called the “drift” speed v, and we say that the electron “drifts” through the metal.
2. So whenever we talk drift speed collisions are taken into account.
3. Drift speed of electrons is very very slow whereas Electric field travels very very fast (I think it is about the speed of light)

Current:

1. Conventional current is the amount of charge (in coulombs) passing that point per second.

n- Number of holes, q – Charge of holes, A - Area of cross section, v is drift speed (v= u E), u – Mobility, E- electric field strength.

2. Electron Current:

1. The rate i at which electrons pass a section of a wire:

2. i = nA v = n A (u E)

3. v is drift speed (v= u E),

4. n is the mobile electron density (the number of mobile electrons per unit volume),

5. A is the cross-sectional area of the wire, and

6. v is the average drift speed of the electrons. In SI units, the units of i are electrons per second.

Answer: Why current is same everywhere in series circuit.

Scenario 1: Connect a battery and a wire as shown in figure.

After connecting the circuit, initially before reaching steady state what happens is:

1. As soon as we connect the circuit, battery creates an electric field as shown in the image (check the electric field of dipole in the image above)

2. Electrons (on negative terminal of battery) start leaving the negative plate and move through the wire to positive plate [that’s how excess charge carriers enter conductor wire].

3. Excess charge resides only the surface of conductor [explanation as to why is given at the end of answer].

4. At the locations marked 1,2,3,4 and 5 initially the electric field direction is as shown below (observe that location 5 is farther than 4, 4 is farther than 3………. It means according to coulombs law location 5 has less field strength compared to 4 and field strength at 4 is less than location 3) Field strength is accordingly represented by the length of the arrow.

5. Observe at right bend, at location 3 more field strength means more force on charge carriers than at location 4.

6. Charge carriers are pushed in the direction of field (as field applies force)

7. Any unbalanced force causes the object to accelerate in the direction of unbalanced force.

8. Hence excess charge slowly starts building up at right bend as more force is applied at location 3 than at location 4. We will call the respective fields as E3 and E4 [E3 > E4]

a. At first few charge carriers build up at right end.

b. But any charged particles can in turn create an electric field. Hence there is an electric field because of surface charge build up.

c. Like charges repel.

d. The direction of this electric field will be opposite (if not exactly opposite, x or y components of vector may also be acting opposite to E3) to the already existing force (which is creating the charge build up) that is because, as more charge carriers are pushed toward one place means it has more charge carrier concentration compared to surrounding locations [electric field is from + to -] . We will call this new field as Eoppto3

e. Now we have two fields acting against each other E3 and Eoppto3.

f. So field strength of E3 reduces because of this.

g. Now what happens to surface charge build up? ……. Surface charge build up started because E3 > E4 ….. …Now after E3 is reduced due to Eoppto3, E3 is little less than previous E3 but still more than E4, hence more surface charge builds up continues.

h. Again Process from b to e repeats.

9.
a. At every surface charge build up episode if E3 still greater than E4, surface charge build up continues…….. Like this at some point E3 will be equal to E4… E3 = E4.

b. It means no unbalanced forces to accelerate charge carriers… means surface charge build up stops when E3 = E4.

10. Not only at this location, In entire circuit, this process keeps happening and at last when the all the electric fields becomes equal (uniform) this surface charge build up stops (if all electric fields are equal, no more unbalancing forces to accelerate charge carriers).

Steady State:

11. Hence at steady state, in this particular circuit, electric field is uniform in entire wire. (at any point if electric field is not uniform, surface charge builds up and makes electric field uniform)

So why is current everywhere same in this circuit?

For a conductor wire of particular metal, number of mobile charge carriers, mobility (u), area of cross section as we have taken is constant then the only varying factor is electric field.

Due to surface charge build up mechanism, electric field also becomes uniform. Means pushing force on charge carriers is everywhere constant. Hence current is same everywhere.

Excess charge carriers are only building up on surface. Conductor has so many free electrons and under uniform electric field, they start moving. Hence these free electrons contribute to current.

Excess electrons are resided on surface and because of them; uniform electric field is maintained (in this circuit without any resistor).

Battery tries to maintain same potential difference across its terminals and hence surface charge build up also stays same as long as the battery works. And as long as this set up stays same, current is same everywhere.

Scenario 2: Battery, (thick) wire and resistor (as thin wire) of same material:

As soon as we connect the battery in circuit initially before reaching steady state what happens is:

1. Initially Electric field in thick wire and thin resistor (mentioning only downside portion of circuit) might about be same (Not exactly equal but about be same because, observe in the image above how electric field lines almost have a circle-ish kind of shape (not exactly of course) and one can notice electric field strength (length of vectors) about be same there.

2. Excess charge carriers (when connected to battery, electrons start leaving negative terminal travels thru wire enter positive terminal, thus excess charge carriers enter wire) start moving due to initially established field.

3. So now charge carriers have to move through thick wire, enter thin resistor and then exit to thick wire.

4. Number of charge carriers per second trying to enter the resistor is large whereas the number of charge carriers per second passing though the thin resistor is small number.

5. So excess charge carriers pile up at the entrance of resistor.

6. Due to pile of charges at entrance of resistor, deficiency is created at the exit location of resistor

7. Note this point, this will be useful to determine when the pile up stops:

a. So why the pile up started? …… Because large number of charge carriers per second entering the resistor and only small number of charge carriers per second are able to leave. . . . why?.... due to difference in areas of cross section [pile up = incoming charge carriers per second > outgoing charge carriers per second]

b. At this point in our analysis, still surface charge is just at the beginning of building up stage and hence electric field is about be same in thick, thin wires and hence same drift speed in both sections of wire….. that’s why large number of charge carriers per second trying to enter the resistor and only small number is able to leave.

8. So the excess charge move to surface and pile up of surface charges begin.

9. Pile up of charge at entrance and deficiency of charge at exit ..….Notice the electric field pattern due to pile up? ……… so an electric field is developed inside resistor having direction from entrance of resistor to exit location.

10. Surface charge carrier pile up at entrance,

a. repels the incoming charge carriers (means speed of those incoming charge carriers decreases)

b. They also repel outgoing charge carriers from resistor, as a result their speed increases.

c. Here observe that as surface charge pile up increase, electric field strength developed by this also increases gradually

11. So after this speed adjust, if incoming charge carriers per second > outgoing charge carriers per second ….. Surface charge pile up continues …….this in turn increases electric field strength developed by these surface charge carriers. And this process repeats till pile up stops.

12. When all the incoming charge carriers per second entering resistors are able to leave resistor at the same rate the pile up stops.

a. How is this achieved?

b. Charge carriers travel with a certain speed till entrance of the resistor

c. At the entrance due to surface charge pile up, field strength is increased in resistor

d. As charge carriers enter resistor, speed of charge carriers increases (as field strength is greater here) and Yes, speed of charge carriers gets increased inside resistor.

e. So whatever large number of charge carriers per second are entering from thick wire are able to leave the thin resistor because of increased drift speed.......after charge carriers leave resistor, electric field is small in thick wires hence speed decreases as thick wires have greater area of cross section. So only inside resistor electric field magnitude is large. In thick wires it is small on both ends of resistor.

Observe that rate of flow of charge became equal in thick and thin wires due to this difference in speed (if it were not equal surface charge would pile up..Only when this rate becomes equal surface charge pile up stops and this creates our required electric field pattern to achieve same current)

(remember, drift speed takes into account collisions, so the doubt that speed may decrease due to collisions can be avoided)

f. Hence this difference in speed in thick and thin wires makes current equal in both wire and resistor.

13. Electric field has uniform large magnitude throughout the resistor and uniform small magnitude throughout thick wires (uniform magnitude is achieved as explained in scenario 1)

Note: Drift Speed (and this is calculated with all collisions taken into account) of electrons depends on electric field. Why it depends on electric field….electric field is a non-contact force…Under external force, object moves. So as field strength increases, drift speed increases. As field is force…more field means more force.

Regarding voltage drop:

1. What is Electric potential ….. it is electric potential energy per unit charge.

2. What is electric potential difference [voltage] = Change in potential energy / Charge

3. What is change in potential energy ?

a. Work done on the charge changes its potential energy to a higher value; and the amount of work that is done is equal to the change in potential energy

4. So voltage (electric potential difference) = work/charge = change in potential energy / charge. Hence we are considering the work done on charges in when calculating the voltage.

5. Electric field has high potential and low potential locations.

6. Based on field arrows, it starts at high potential and reaches low potential.

7. Whenever charge carriers travel in electric field(not against…moving against electric field requires external force and this increases the potential energy) from high potential to low potential locations, they lose potential energy.

8. Energy is conserved, means potential energy is converted to heat, light etc in circuit.

9. In resistor, observe in the last image that electric field strength is greater than in wires due to surface charge build up. Hence more potential energy is lost here. (and converted to other forms …if load is bulb it converts to heat and light etc)

Scenario 3:: Resistor with same area of cross section and decreased mobility (due to resistor being made with other material than in wires) can also be proved as scenario 2.

Surface charges gets buildup at surface of resistor, electric field increases and same procedure as scenario 2 follows.

---

Surface Charge:

1. If conductor has acquired an excess charge, the excess charge quickly distributes only over the surface of conductor and not anywhere else.

2. Conductor is initially neutral, no of electrons = number of protons. Although the roaming electrons repel each other strongly, this repulsion between electrons is neutralized on the average by the attractions exerted by the positive atomic cores

3. When excess electrons are acquired, [like charges repel] hence excess electrons want to minimize the repulsive forces.

4. According to coulombs law as distance increases force decreases, hence they will want to go as far as possible. Hence excess charge will reside on the surface of the conductor.

5. Moving left or right in the conductor does not help to minimize repulsive forces as it repels from other electrons present there inside conductor.

Electrostatic field inside a conductor is zero here in the image.

Drift speed:

1. A mobile electron in the metal, under the influence of the electric field inside the metal, does accelerate and gain energy, but then it loses that energy by colliding with the lattice of atomic cores, which is vibrating because of its own thermal energy and acquires more thermal energy due to the collisions of the electrons with the lattice. After a collision, an electron again gets accelerated, and again collides.

2. The average speed of an electron in this start–stop motion is called the “drift” speed v, and we say that the electron “drifts” through the metal. So whenever we talk drift speed collisions are taken into account.

3. Drift speed

Current:

Conventional Current I:

It is defined as the amount of charge (in coulombs) passing that point per second. This is the number of holes per second multiplied by the (positive) charge q associated with one hole:

I = q n A v (coulombs per second, or amperes)

I = q n A (uE)

1 C/s = 1 ampere (abbreviated A). The direction of conventional current is opposite to the direction of electron current

n- Number of holes, q – Charge of holes, A - Area of cross section, v is drift speed (v= u E), u – Mobility, E- electric field strength.

Note: Reference: pics, explanation: matter and interactions by Chabay and Sherwood

Answer 5

Why does voltage drop in a series circuit but current stays the same?

If current (*) decreased at location X, then charge would accumulate at location X. This charge would affect the electrical field. It would "deter" the current flowing into X and encourage current flowing out of X. So, in a very short time, the current into X would equal the current out of X. The current would become the same. This happens in incredibly short periods of time,

(*) [By current, I mean conduction current. At this point all you need to know is that I am using your common sense concept of current, as the flow of charges.]

Regarding voltage. The force on a charge that causes it to move in a given direction is proportional to the difference in voltage between two points. (divided by the distance between those points). If voltage did not change from one point to another, there would be no force on the electrons, and they would stay at home watching TV instead of leaving their home and going to work.

Answer 6

Let's assume we have exactly one resistor in the circuit.

Now, note that AFTER the resistor the electromotive force (voltage) is fine to be much weaker than BEFORE the resistor because AFTER the resistor there is NO MORE further resistance (thus no "opposite force") till the very end of the wire. In other words - no longer so much voltage is needed to PUSH electrons through that remaining part of the wire because they are free to go and exit the wire effortlessly (without further obstacles).

Let's imagine that electrons could hypothetically even stop altogether - but: 1) there is some little amount of remaining voltage coming out of that resistor which still slightly pushes them; 2) the remaining RESISTANCE/OPPOSITE force is also much weaker (remember - the other end wide-open) so the electrons flow is "allowed" to achieve the same rate. This is both about the pushing force (voltage) AND the opposite force (resistance still waiting ahead) which have impact on the in-between section of the conductor and contribute to overall constant current rate throughout the whole circuit.

This is exactly how water behaves in a pipe. Before a partially-closed valve (with a very tight slit left open - a resistor) the pressure (voltage) must be very high to squeeze the water volume through the narrow slit in a given time period. On the other hand behind the valve the pressure is already much weaker (most of its initial energy was stopped by the valve) but still the same volume of water (current) flows through the pipe because no more valves/resistance ahead block the flow so nothing must really push the water so hard and the resulting speed of molecules is the same. Much weaker push but also much wider exit - yields the same current rate. This is just how both hydraulics and electricity work.

And the beautiful thing is that the same plumbing analogy works with whatever number of resistors (valves) in both serial and parallel circuits and for all the quantities involved (pressure/voltage, current, power, etc).

I hope this will help you to look at these mechanisms from more satisfying angle. Good luck!