Resistance and Current: Does A1 = A2?

[physics kiddy]

I have posted a pic of my question.

Suppose there are two ammeters A₁ and A₂ placed in a circuit as shown in the diagram. I want to know if the reading of A₁ is same as that of A₂. Books say that it is. But my logic is that since current crosses a resistor it gets lowered. Hence A₁ > A₂. Please explain me what is true and why.

 

[daveb]

Think of it this way - can charge go anywhere else other than around that one loop?

 

[FOIWATER]

The current is the same anywhere in that loop, and is a total function of total circuit impedance, and source voltage.

The voltage is what gets dropped across the resistor, not the current, but the amount of voltage that is dropped, does depend on current. Voltage is a measure of electrical potential energy, and is measured in Joules/Coloumb.

Kirchoff's Voltage Law is a physical law that states that the sum of voltage drops around your loop equates to your source voltage.

Ohm's law gives a mathematical relationship of voltage to current and impedance.

V = IR where V is voltage measured in volts, I is current measured in amperes, and R is resistance measured in ohms.

The source voltage divided by the resistance, will yield the total circuit current, that for a series circuit, is the same value of amperes at any point.

 

[sophiecentaur]

Thinking of Current as a flow of charge around a circuit, if you move some charge into one part of a circuit then that excess charge will be pushed around to other parts of the circuit. To achieve just a small imbalance in charge (as across a capacitor, for instance) requires a lot of effort. If a steady current were flowing around the circuit and it didn't 'even out' around the loop, the whole thing would explode with attractive and repulsive forces involved as more and more charge built up in one place.
Current In = Current Out is the rule.
What DOES get less as you go round a circuit is the Potential difference - as energy is dissipated in the various loads (resistance etc.).

 

[davenn]

I have posted a pic of my question.

Suppose there are two ammeters A₁ and A₂ placed in a circuit as shown in the diagram. I want to know if the reading of A₁ is same as that of A₂. Books say that it is. But my logic is that since current crosses a resistor it gets lowered. Hence A₁ > A₂. Please explain me what is true and why.

In a series circuit like that one, the current is not dropped by the resistor, instead it is limited by the resistor, is the same no matter where it is measured
Its the Voltage that drops across the resistor
lets look at your circuit with some values added

Using Ohms Law, what do you think the current flowing in the circuit is ?
hint... I = V/R
That will be what is measured by each Ammeter

now look at the resistor, what is the voltage at point arrowed A, and what about the point arrowed B ? and why ?
Now that you have worked out the current flowing in the circuit, use Ohms Law again and work out the Voltage drop across the resistor hint ... V = I x R


Dave

 

[physics kiddy]

In a series circuit like that one, the current is not dropped by the resistor, instead it is limited by the resistor, is the same no matter where it is measured
Its the Voltage that drops across the resistor
lets look at your circuit with some values added

Using Ohms Law, what do you think the current flowing in the circuit is ?
hint... I = V/R
That will be what is measured by each Ammeter

now look at the resistor, what is the voltage at point arrowed A, and what about the point arrowed B ? and why ?
Now that you have worked out the current flowing in the circuit, use Ohms Law again and work out the Voltage drop across the resistor hint ... V = I x R


Dave

Dave, you wrote resistors limit the current and don't drop it. Let's assume that 10 amps of charge flows through the circuit. What happens to the current when it reaches the resistor ?

 

[davenn]

Dave, you wrote resistors limit the current and don't drop it. Let's assume that 10 amps of charge flows through the circuit. What happens to the current when it reaches the resistor ?

Ahhhh but there isn't 10 Amps flowing in the circuit (this circuit) there is ONLY 1 Amp and that is determined by the resistance (read as LOAD) across the power supply You didnt do the math with the formula huh ?? ;)

You are hinting at a query many people make...

they say " I have this 5 amp power supply but my circuit only needs 0.5A (500mA), can I use this power supply? "

They think that the 5Amps is going to blow up their circuit than doesn't need that much current
The LOAD may be just one resistor as in my circuit above or it could be a complex circuit consisting of many components, resistors, capacitors, transistors etc that equal that 10 Ohm resistance.

A practical example from my workshop...

I have a Ham radio transceiver, it is connected to a power supply capable of 40 Amps.
BUT there isn't 40 amps flowing through my radio. In receiver mode there's around 1.5 Amps,
and in transmit with 100W RF output power it has ~ 20Amps of current flowing.
I use a power supply capable of much more current, as wisdom dictates that having that extra "headroom" my power supply is never going to be working hard at full output. It will be just idling.

did that help your understanding ? :)

Dave

 

[davenn]

the say " I have this 5 amp power supply but my circuit only needs 0.5A (500mA), can I use this power supply? "

They think that the 5Amps is going to blow up their circuit than doesn't need that much current
The LOAD may be just one resistor as in my circuit above or it could be a complex circuit consisting of many components, resistors, capacitors, transistors etc that equal that 10 Ohm resistance.

Now I will just qualify this statement that I made...

The circuit will ONLY draw that 0.5Amp IF and only IF it is using a power supply of the correct voltage rating. As you increase the voltage of the power supply then the current is also going to increase proportionally. Eventually you will get to a point when components in that particular circuit fail and you will see smoke.

So in that circuit above I had a 10V supply and a 10 Ohm resistor
do the math and work out the current flow, then double the voltage to 20V and work out the new current flow
What is it now ?

cheers
Dave

 

[davenn]

now here's another interesting sideline thought for you...

That transceiver of mine runs off 13.8VDC, its drawing 20 amps to produce 100 Watts of output power. Power (Watts) = Volts x Amps = 13.8 x 20 = 276 Watts
What do you suppose is happening to the other 176 Watts ?

Dave

 

[anuragkanase]

What do you suppose is happening to the other 176 Watts ?

Dave

Is it heating?

 

[anuragkanase]

I meant is it generating heat?

 

[davenn]

yup and lots of it. I guess i could do calculations on what power is being used by other circuitry. But I would bet that at least 130W of that 176W is just waste heat. Hence why the output transmitting transistors are on a large heatsink :)

scarey huh!

Dave

 

[anuragkanase]

Liked the answer. Salute buddy.
Let's iron out of the waste energy.

One more thing,
Can you explain this clearly:

In a series circuit like that one, the current is not dropped by the resistor, instead it is limited by the resistor, is the same no matter where it is measured

 

[physics kiddy]

Dave, I understand you. I am sorry I had not used any calculation in that question. I am back with the question even clearer. I have attached the pic.

In the circuit I have drawn, 10 amps of current flows. Voltage is 10 V and resistance of R₁ is 1Ω. This time I have used calculations. My question is the same. What happens to the current when it flows through the resistor. From my knowledge I know that the current flowing through point 'A' in the diagram at any instant is 1 Coulombs. Then how much current flows through the resistor ? Is it 1 Coulomb. If it is then why ?

 

[anuragkanase]

I am sorry to interrogate, but the unit of current is Ampere, and coulomb is unit of charge. As per ohms law, 10A Current will flow, to balance the equation.

 

[davenn]

you didnt attach the pic :)

anyway 1 Coulomb = 1Amp of current past a given point in 1 sec
but there's no need to bring coulombs into these discussions it will only confuse thing more. just keep it to Amps, Volts and Resistance

OK as per your description...

If the voltage is 10V and the resistance is 1 Ohm then the current flowing around the circuit is 10 Amps

I = V / R = 10V / 1 Ohm = 10 A the resistor is going to get VERY hot!

This of course assumes that the battery is capable of supplying 10 Amps !

cheers
Dave

 

[physics kiddy]

Cheers !

 

[physics kiddy]

So, shall I conclude that resistors limit (decrease) the speed of flow of electrons ?

 

[sophiecentaur]

A resistor transfers energy. It is not like a thin hose pipe - very bad analogy when discussing electrical current in terms of electron flow.
A 1V supply, when connected to a 100Ω resistor, will dissipate 1/100W of power. If you connect a 200Ω resistor then there will be half the current so the power will be 1/200W.
There isn't really a satisfactory way to 'explain' what happens except to say that, as Current flows through a resistor, the electrons interact with all the atoms and lose Potential energy on the way through. The last thing you must think is that it's something to do with the Kinetic Energy of some massive flowing liquid and conventional Dynamics.

So ... NO.

 

[physics kiddy]

A light bulb is a resistor. It transfers electrical energy into light and heat energy. But, what actually happens to electrons when they pass through a resistor. Do they loose energy and stop there or their count decreases when they leave the resistor ?

I have attached a pic.

I have assumed that 10 amps of current is flowing through the circuit. What happens to them when they reach the resistor ? 'A' stands for ammeter.

 

[davenn]

A light bulb is a resistor. It transfers electrical energy into light and heat energy. But, what actually happens to electrons when they pass through a resistor. Do they loose energy and stop there or their count decreases when they leave the resistor ?

I have attached a pic.

I have assumed that 10 amps of current is flowing through the circuit. What happens to them when they reach the resistor ? 'A' stands for ammeter.

A lamp is a little like a resistor, yes it has resistance but that changes between its cold and hot condition, also resistors normally don't emit light, unless they are getting that hot that they start to glow red just before they fail.

Basically... In a lamp when energy (an electric current) is put into the tungsten filament, that additional energy causes some of the electrons of the tungsten atoms to move to a higher energy level. When those electrons drop down to their normal level, they loose energy, some of that energy is released as photons (light) some of it as heat.

You can't assume that there is 10 amps flowing as you have given no other info to substantiate that.
You need to tell us what the battery voltage is and you need to tell us what the resistor value is THEN you can work out what the current flowing is. THEN you can work out what else might be going on in the circuit ... for example how may Watts of energy is being converted to heat in the resistor etc

Reread my posts #5 and #7 :) they obviously haven't quite been understood yet ;)

Dave

 

[sophiecentaur]

A light bulb is a resistor. It transfers electrical energy into light and heat energy. But, what actually happens to electrons when they pass through a resistor. Do they loose energy and stop there or their count decreases when they leave the resistor ?

AS I said, don't think of electrons as fast moving objects carrying Kinetic Energy around from battery to resistor. It's just the wrong picture. When you are pedalling your bicycle, the links in the chain don't get used up, do they? They all go round the circuit at the same speed, even. They are very lightweight so it can'tbe their KE that gets transferreedfrom foot to wheel. That analogy applies (in a very limited way) to the electron flow. Remember, the mean drift speed of electrons carrying a current is only about 1mm/s, compared with their RMS velocity of hundreds of m/s.

A lamp is a little like a resistor, yes it has resistance but that changes between its cold and hot condition, also resistors normally don't emit light, unless they are getting that hot that they start to glow red just before they fail.

Basically... In a lamp when energy (an electric current) is put into the tungsten filament, that additional energy causes some of the electrons of the tungsten atoms to move to a higher energy level. When those electrons drop down to their normal level, they loose energy, some of that energy is released as photons (light) some of it as heat.

Dave

I have to take issue with that. You are implying that the conductor is like a simple gas, with separate atoms and electrons around them. The interaction of conduction electrons with the metal structure is not localised. The interaction is with many atoms in the locality of an electron and causes vibration and an increase in the mean energy of all the other electrons which are moving in all directions with a very high RMS velocity (thermal energy, if you like). The energy level changes involved are extremely low and do not all correspond to electron/atom energies. The only time this is the case is when there is an arc on the surface of a metal and high speed electrons are bashing at the atoms.

 

[davenn]

so you have a new theory on how electrons emit photons without the input of energy ? ;)

the energy level changes must be high enough for that emission to take place


D

 

[sophiecentaur]

My issue is that you imply that the electrons involved in conduction or in light emission in a solid are interacting with individual atoms. They interact with the whole structure and not just 'an atom'. In condensed matter the energies are not in discrete levels, they are bands.