Why is voltage divided among resistors when they are connected in series?

Question

Why is voltage divided among resistors when they are connected in series while it is not when connected in parallel?

Answer 1

When resistors are in parallel the total resistance is found by 1/Rtotal=1/R1+1/R2....  and then solve for Rtotal by the inverse.

When resistors are in series you just add up the resistance in order to find the total.

But to answer your question:

Ohms law says   Voltage=Current*Resistance

You use this to solve for paralled and series.  Just in parallel you have to consider the Total resistance of the two that are their.  and use that total in the formula.

If the battery is 12 volts then the voltage throughout added up should always equal 12 volts.

Answer 2

I am going to try to simplify for you like I do my students.

First think in terms of voltage being pressure, like the water pressure at your house.

Now think if current being or the amount of flow, like water or any fluid flowing.

Now think in terms of resistance being a restriction to that flow.

Now when you apply power to a series circuit. The flow hits the first resistor.  It has the full amount of pressure the source is putting out.

As the flow if forced through the resistor which is a restrictor it looses some of the pressure behind because of the amount of pressure it takes to push the flow through the restriction. [in this case a resistor]

The voltage drop you measure across the resistors is how much pressure you are losing by the restriction to flow of that resistor.

A good experiment that will help you see it is:

Get two standard water hoses:

Get  two water pressure gauges you can s***w into a standard water hose.

Get a value you can s***w into a standard water hose.

Get a standard adjustable nozzle.

Now s***w one of the pressure gauges onto the water hose. Next s***w in the value,  Next s***w in the other pressure gauge.

Next s***w in the other water hose and put the nozzle on the end of it.

turn on the water all the way with the valve open all the way.

Adjust the nozzle until you have a good spray.

Now start slowly turning off the valve while watching the two pressure gauges.

You will observe that as you close the valve the pressure you read on the other side of the valve starts dropping and is less that the pressure gauge on the side of the valve connected to the facet is reading.

The difference is the pressure loss caused by the increasing restriction as you slowly turn off the valve.

That is the sample principal as the voltage you measure across a resistor in a series circuit.

The voltage you are measuring across the resistor is the amount of Electro Motive Force [or pressure] loss caused be the restriction to current flow by the resistor.

I tried to stay away from a lot of math and formulas because if you are like a lot of my students diving straight into a bunch of Math and formulas without really understanding what they are for will just get you more confused.

Answer 3

in electrical circuits ohm's law v=ir should hold in all cases.

therefore,when two quantities in this equation change with respect to each other ,the third must remain constant.

in case of a parallel combination,the voltage applied is the same across all resistors ,hence the current gets divided among the resistors according to the current divider formula.

in the case of a series arrangement,the current is the same through all resistances,hence the voltage gets divided among the resistances according to the voltage divider formula.

Answer 4

Two ways to get to the same conclusion for a series circuit:

1. Conservation of energy.  The resistors span across a potential energy difference measured by V volts.  Moving across one resistor requires an amount of energy less than V volts, same with each subsequent resistor.  In the end, energy has to be conserved so the total energy consumed by going through all the resistors has to be the potential difference across the entire series chain.

2.  Conservation of charge & Ohm's Law:  The amount of charge per unit time (current) passing through any of the resistors in a series circuit is the same for all of them.  If not, charge is being lost or added somewhere in the circuit and it is no longer a series circuit.  Since current is the same through all the resistors, the voltage across each resistor is just Vn = I*Rn  where Rn is value of the nth resistor and Vn is teh voltage across the nth resistor.  Summin up all teh voltages:

V = V1+ V2 +...+ Vn = I*R1 + I*R2+...+ I*Rn = I*(R1+R2+..Rn)

Hence agian by conservation of enery and current V will be the voltage across the circuit.

Now for a parallel circuit you have many paths to go from high potential to no potential (or ground).  So each resistor in parallel has the same potential difference across it.  Ohm's law holds in each parallel branch so each resistor has a current In through it givne by:

In = V/Rn where now V is the voltage across teh circuit.