# 3 lamp circuit

Hi guys.

I need some help with an assignment. I have a circuit as depicted below with a 220V AC power source and 3 100W lamps. I’m asked to calculate the power in each lamp when switch 4 is closed and when switch 5 is closed. I’m also asked whether the lamps are brighter or dimmer.

I’m thinking that lamp 1 will always burn at same brightness, since it’s parallel to the other lamps. However I am confused whether lamp 2 will work when switch 5 is closed. My first reaction is no, but I’ve managed to confuse myself enough to not know anymore.
So pls help.

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verty
Homework Helper
About lamp 2, current will only flow through a resistor where there is a potential difference (voltage). If switch 5 is closed, the same piece of wire connects both sides of lamp 2, so there will be no voltage across lamp 2 and therefore no current through lamp 2.

As for the brightness of 1, that depends on the voltage across bulb 1 (according to Ohm's law).

>provided that wires have 0 resistance< ... you are right that bulb 1 will glow at same brightness.

And as vertigo said, due to 0 potential drop across bulb 2(switch 5 closed) ... it will not glow.

Also, this will not be true for long time,
after a while, bulb will heat too much increasing its resistance and therefore increasing its power consumption and brightness.

Assuming ideal conditions of course, resistance in wire = 0 etc.

As I understand, when 1) switches 4 and 5 are closed then bulb 1 will glow the same as if 4 was open, that means at 100W and bulb 3 will also be at 100W, bulb 2 will not work. The voltage drop across the bulbs will be 220V, since they are in parallel and the voltage source will put out twice the current as it would with only one bulb. Is this correct?
2) only switch 5 is closed then it will be just the same as if switches 4 and 5 open, with bulb 1 at 100W at the other two bulbs not working. As you have said.
3) only switch 4 is closed then all bulbs glow. Bulb 1 will be the same brightness it always was. But what about the other two? As I understand the voltage drop accross both, bulb 2 and three together is 220V, that means 110V each? But my main question is about the currents. How much current is put out by the source and how do the current distribute? 1/2 both lanes or 1/3 and 2/3?

Thanks a lot for the help, by the way. I appreciate it.

verty
Homework Helper
Parts 1 and 2 are correct. For part 3, you would need to calculate the equivalent resistance of the two bulbs, to get the current through that branch.

It is true that the voltage will split between the bulbs because they are identical, but you shouldn't rely on that. In many problems, they won't be identical.

Use the formulas for series and parallel resistors to calculate the equivalent resistance.

$$R_s = R_1 + R_2,$$
$$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}.$$