Originally Posted by north

I think I have understood why the 4th resistor must be included.

what I did was 4/3= 1.33333W. but what I also did was take 0.33333 and *20 and got = 6.666W.

so what 0.33333 represents is that for every 1 watt that was originally there(20W) , there is an increase per watt of 0.33333 of the total original wattage because the 4th resistor is no longer considered. and this makes sense since the current in the circuit has increased.

so now if we take the answer of 4/3=1.33333*20=26.6666 and then 26.6666/3=8.8888W=8.89W

is my thinking sound here?

Yep, that makes sense to me, except 4/3 does not equal 1.33333 Watts. 4/3 is just the ratio of the number of resistors you started with to the number you ended with. It has no units.

Originally Posted by north

I think I have understood why the 4th resistor must be included.

what I did was 4/3= 1.33333W. but what I also did was take 0.33333 and *20 and got = 6.666W.

so what 0.33333 represents is that for every 1 watt that was originally there(20W) , there is an increase per watt of 0.33333 of the total original wattage because the 4th resistor is no longer considered. and this makes sense since the current in the circuit has increased.

so now if we take the answer of 4/3=1.33333*20=26.6666 and then 26.6666/3=8.8888W=8.89W

is my thinking sound here?

As I wrote earlier, the 4th resistor must be included since that is part of the initial data, ie. 20W is being dissipated in the 4 resistors. This is your starting point.

You did not need to do the 0.33333 part.

As Ron suggested, the current has increased by a factor of 4/3.

Since P = V * I and V is constant, then P has increased by the same proportion. So P3 = 4/3 * 20. Hence for one resistor the power is

4/3 * 20/3 = 80/9 = 8.89W.

Originally Posted by north

thanks Ron and ljcox for making me think and your both your time.

as always appreciated

north

You're welcome.

Originally Posted by north

I just did not get , at the time , the significance of the 4th resistor, even though it was shorted..

You still don't understand the process.

Initially the 4th resistor is NOT shorted. The resistors are assumed to be equal and are dissipating a total of 20W. These facts lead to the first equation (see my maths or do it yourself).

THEN you short one resistor and write the second equation.

Then you eliminate the unknowns and find the power dissipated by the 3 resistors. Finally divide by 3 to obtain the per resistor dissipation.

Originally Posted by north

I just have to get use to, at times , thinking in terms of ratio or porportion. right now its not easy for me to do. it will take time I just hope not to long.

There is more to it than ratios and proportions.

I did not simply accept Ron's (no offence to Ron) statement that the currents are in a 4/3 ratio. Firstly, I wrote down the equations and proved that this is true.

I suggest that you do the same.

Originally Posted by ljcox

I did not simply accept Ron's (no offence to Ron) statement that the currents are in a 4/3 ratio. Firstly, I wrote down the equations and proved that this is true.

Len I didn't just make an unsubstantiated statement. I wrote:

P4=V^2/(4*R)=20
P3=V^2/(3*R)
therefore,
P3/P4=4/3
P3=P4*(4/3)

No offense taken.

Ron,
Sorry, I wrote my post from memory, I should have re-read your post, ie. the one I had in mind.

I just re-read it and you did not actually say the currents were in a 4/3 ratio, you asked North to determine what the ratio is.

That's what I did, I did the maths to show that the currents are in a 4/3 ratio.