DC Equivalent Circuit: Resistor vs Cell

[amaresh92]

please could you tell me that ,In dc equivalent circuit the resistors are replaced by cell.why is it so?though the resistor gives voltage drop where cell provides a emf then how does these are equivalent?
thanks.

 

[vk6kro]

Maybe you should give an example.

Resistors are not the same as voltage sources, but there are similarities.

If a resistor has a large current passing through it, and you place a much larger resistor across the first one, it will have almost no effect on the voltage across the first resistor and will draw a current as if it had been placed across a voltage source.

 

[amaresh92]

Maybe you should give an example.

Resistors are not the same as voltage sources, but there are similarities.

If a resistor has a large current passing through it, and you place a much larger resistor across the first one, it will have almost no effect on the voltage across the first resistor and will draw a current as if it had been placed across a voltage source.

what will happen when a smaller resistor is connected across the first resistor?

 

[vk6kro]

You really need to accept the initial conditions for this to work.

Suppose you had a radio that normally ran off 6 volts from 4 "C" cells.

All you had was a 12 volt battery from a car and two 12 volt rear lamps, also from a car.

The lamps draw 3 amps if placed in series across the 12 V battery. So they have a resistance of 4 ohms total or 2 ohms each.

Across each of them is 6 volts. Now if you connect the radio across one of the lamps, it may draw 50 mA or 10 mA depending on how loud the sound was.

If it drew 50 mA at 6 volts, it has a resistance of 6 V / 0.05 A = 120 ohms.

If you put this across one of the lamps, the resistance of the pair would be 1.97 ohms.

This would cause the voltage to drop from 6 volts to 5.95 volts.

So, the car lamp is behaving just like a source of EMF and giving a very stable voltage.
It is very inefficient to do this, but it gives a result.

 

[amaresh92]

You really need to accept the initial conditions for this to work.

Suppose you had a radio that normally ran off 6 volts from 4 "C" cells.

All you had was a 12 volt battery from a car and two 12 volt rear lamps, also from a car.

The lamps draw 3 amps if placed in series across the 12 V battery. So they have a resistance of 4 ohms total or 2 ohms each.

Across each of them is 6 volts. Now if you connect the radio across one of the lamps, it may draw 50 mA or 10 mA depending on how loud the sound was.

If it drew 50 mA at 6 volts, it has a resistance of 6 V / 0.05 A = 120 ohms.

If you put this across one of the lamps, the resistance of the pair would be 1.97 ohms.

This would cause the voltage to drop from 6 volts to 5.95 volts.

So, the car lamp is behaving just like a source of EMF and giving a very stable voltage.
It is very inefficient to do this, but it gives a result.

thanks a lot for your nice explanation.

 

[sophiecentaur]

please could you tell me that ,In dc equivalent circuit the resistors are replaced by cell.why is it so?though the resistor gives voltage drop where cell provides a emf then how does these are equivalent?
thanks.

They are not really equivalent at all - despite the fact that you can measure a potential difference across them both. A cell is a source of power and a resistor is a dissipator of power. All you can say is that, in any circuit, under a specific set of conditions, the values of voltage and current in that circuit will be the same IF you replace the resistor by a cell with the same voltage. It can even apply for AC, if your 'voltage source' has the right signal on it.

What I'm saying is that the concept of 'equivalent circuit components' is for analysis and not really intended to be applied practically. I remember, when I was very young, looking at a complicated equivalent circuit for a transistor, with all sorts of current and voltage sources in it, and being laughed at (much derision from fellow students, of course), when I suggested you could "build" a transistor that way.

 

[amaresh92]

They are not really equivalent at all - despite the fact that you can measure a potential difference across them both. A cell is a source of power and a resistor is a dissipator of power. All you can say is that, in any circuit, under a specific set of conditions, the values of voltage and current in that circuit will be the same IF you replace the resistor by a cell with the same voltage. It can even apply for AC, if your 'voltage source' has the right signal on it.

What I'm saying is that the concept of 'equivalent circuit components' is for analysis and not really intended to be applied practically. I remember, when I was very young, looking at a complicated equivalent circuit for a transistor, with all sorts of current and voltage sources in it, and being laughed at (much derision from fellow students, of course), when I suggested you could "build" a transistor that way.

thanks, your explanation helps me much.