Physics Question. Desperately need help.?

Question

The circuit in the drawing contains five identical resistors. The V = 45 V battery delivers 44 W of power to the circuit.

http://www.webassign.net/CJ/p20-63.gif

I've been struggling with this one for several hours now and still cannot solve it. Can anyone give a concise and clear explanation of how to arrive at the correct answer? I'd really appreciate it.

I am looking for the answer as R in ohms. Thanks.

Answer 1

This is how I worked it out:
1. From W = V²/R, find the equivalent resistance of network.

Req = 45²/44 = 46.0227 Ω.

2. Reduce the network to its equivalent resistance:
Knowing that two equal resistors R in parallel offer an equivalent resistance of ½ R, resulting resistance when 2 R is connected in parallel with this, is ½ R × 2 R/(2 R + ½ R) = R/2.5 = 0.4 R.
Total equivalent resistance is then 1.4 R.

3. Equate both results, then solve for R.
R = 46.0227 Ω/1.4 = 32.8734 Ω.

As a check, you may compute total equivalent resistance again, in terms of its numerical value. This should yield 46.0227 Ω.

Answer 2

Don't know what are you looking for. Assume you want R.

Call each resistance R.
R2 and R5 in parallel gives an equivalent resistance of 1/2 R. This is now in parallel with R3+R4 = 2R. The equivalent resistance is now between 1/2 R and 2R and you get 2/5 R.

This is now in series with R1. Total resistance Rt is 7/5 R.

Separately, Power = V^2/Rt, ie, Rt = V^2/P

Equate 7/5 R = 45^2/44, or R is 32.8ohm

No simple answer.

Another way is to estimate.

Power= V*I. Since 45 and 44 are very close, you can estimate that current I to be almost 1 amp,

Rt = V/I, so Rt is about 45/1 = 45 ohm

Equate 7/5 R = 45, you get R = 5*45/7 = 32 ohm

Answer 3

What is the question?

I guess you are looking for the value R of the resistor.

Well for one thing you know the current through the battery
P = Vi so I = P/V
I = 44/45 A

To compute the overall resistance you take it one step at a time.

1st the 2 rightmost branches with r3, r4 and r5. Using the formula for parallel resistor R1 and R2:
Req = 1/(1/R1 + 1/R2)
Here
Req = 1/(1/R + 1/2R) = 1/(3/2R) = 2R/3

Add in the branch with R2

Req = 1/(3/2R + 1/R) = 1/(5/2R) = 2R/5

Add in the R in serie

Rtotal = 2R/5 + R = 7R/5

Now Rtotal = V/I
So 2R/5 = 45/(44/45) = 45^2/44
R = 45^2/44 * 5/2 = 115 Ohms

Answer 4

Get the formulas for Rt.

1)Rt=Vt/It
2) Rt= R1 + (1/R2 +1/R3+R4 + 1/R5)^-1

All R's are equal (except for Rt, of course)
equate 1) and 2)
You'd get 0.731ohms