phys1002_sln03_sm2_2007B

phys1002_sln03_sm2_2007B - PHYS1002 TUTORIAL 3 SOLUTIONS...

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1 PHYS1002 TUTORIAL 3 SOLUTIONS Semester 2, 2007 1. COMBINATIONS OF RESISTORS (a) Let the resistance of each resistor be R and let the emf of the battery be ε . When the resistors are coupled in series, the equivalent resistance is R s = R+R = 2R. By Kirchhoff’s loop rule, the voltage drop across the equivalent resistance equals the emf of the battery ε. The total power dissipated in the resistors (which equals the power delivered by the battery) is then 2 2 20 . 2 s s P W R R ε = = = If instead the resistors are coupled in parallel, the equivalent resistance is R p , where 1/R p = 1/R + 1/R = 2/R, i.e. R p = R/2. The voltage drop across the equivalent resistance is again equal to the emf of the battery, and the total power dissipated in the resistors is again equal to the power delivered by the battery. Thus the total power is now given by 2 2 2 2 2 2 2 20 80 p s p P P W W R R = = = ⋅ = ⋅ ⋅ = . So the power dissipated for the parallel combination (which has the lower equivalent resistance) is 4 times greater than for the series combination. It is also possible to solve this problem without first introducing equivalent resistances. It can e.g. be done as follows: For the series combination, the voltage drop across each resistor is ε/2, since both resistors are identical and the sum of the voltage drops in the series combination has to equal the emf of the battery. The total power dissipated is the sum of the dissipated power in each resistor: ( 29 ( 29 2 2 2 / 2 / 2 20 . 2 s P W R R R = + = = For the parallel combination, the voltage drop across each resistor is ε. Therefore the total power dissipated is now 2 2 2 2 4 p s P P R R R = + = = which is (of course) the same result that we got from the first method. (b) The two top resistors are coupled in series; the equivalent resistance is R top = R+R =2R. The two bottom resistors are also coupled in series with the same equivalent resistance, R bot = R+R = 2R. The resistances R top and R bot are coupled in parallel, so the equivalent resistance of these, call it R eq , is given by 1/R eq = 1/R top + 1/R bot = 1/(2R)+1/(2R)=2/(2R)=1/R, i.e. R eq = R. This is the equivalent resistance between points a and b, which therefore equals R.
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2 2. KIRCHOFF’S RULES (a) Circuits reducible to a single loop. (i)
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This note was uploaded on 11/29/2011 for the course PHYS 1002 taught by Professor Tarasplank during the Three '11 term at Queensland.

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phys1002_sln03_sm2_2007B - PHYS1002 TUTORIAL 3 SOLUTIONS...

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