number 6 5. At the most recent meeting of the physicists who look-to-torture stu

Question

number 6

5. At the most recent meeting of the physicists who look-to-torture students club, there was great discouragement at how the students had solved the evil capacitor network problem. What could be done? A timid voice from the back said, "We could try again with resistors? Yes... resistors! Mwa-ha-ha-ha! Find the equivalent resistanee of the network pictured here, then find the current and potential difference across each resistor. 6. Weekend breakfast! You love waffles, have to have your co and well, bacon because it is bacon! Your coffee pot draws 800 W of power, the waffle iron is rated at 12 W and your frying pan is also drawing 1200 W. All three are into wired on the same household V circuit. Calculate the current in each appliance, and determine whether your breakfast plan will be foiled by a 25-A circuit breaker.

Explanation / Answer

Req= R1 + [R2 || (R5 + ( R3||R4))]

Req= 7 + [4 || (3 + ( 2 || 2))] = 7 + [4 || (3 + 1)] = 7 + [4 || 4] = 7 +2 = 9

Ieq= I1 = V/req = 9V/9 = 1A --------------(1)

By KVL at point a,

I1= I2+I5 ---------------(2)

Since R2 and R345 are in parallel combination,

V2= V345

I2*R2= R345*I5

I2/I5 = R345 R2

R345= (R5 + ( R3||R4) = (3 + ( 2 || 2))= 3 || 1 = 4

I2/I5 = R345 R2 = 4/4 = 1

Thus I2= I5 --------------(3)

Plug (3) in (1)

I1= 2*I2

Give I2= I1/2=1/2= 0.5 A

Thus

I2= I5 = 0.5 A

Now Since V3=V4

I3*R3= I4*R4

I3/I4= R4/R3= 2/2= 1

Thus I3/I4= 1 => I3=I4

By KCL at point c,

I5= I3+I4= 2I3

I3=I4= I5/2= 0.5/2 = 0.25 A

Thus I1= 1.0A, I2=I5= 0.5A and I3=I4=0.25A

Wnet = Vnet*Inet

Inet = Wnet/Vnet = (800+1200+1200)/120 = 26.7 A

Since Inet is greater than the circuit breaker current, breakfast will be foiled.

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