Unformatted text preview: 7B.S11.D Quiz 3 DL section _ Last 6 digits of student ID
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________________ ________________ First three letters of your last name ___ N o boo k s o r not es. C a l c u l a t o r s O K . Show a l l you r w o r k b e l ow. A nsw e r s a l on e w i l l r e c e i v e no c r e d i t !
R4 = 3 a) In the circuit to the right, which resistor, R1 or R5, will have the greater thermal power?
Explain briefly. (No calculation needed).
P = I Delta(V) and Delta(V) = I R so R5 = 2 P = I R^2 Because I is the same (it's the same wire from R_5 to R_1) and R_1 is
bigger than R_5, then R_1 will have the greater thermal power. R1 = 7 R2 = 4 R3 = 24 ! b) Find the equivalent resistance of the circuit. Show your work.
R_1 + R_4 + R_5 are in series, then R_3 is in paraller with the 1,4,5 triplet.
R_145 = R_1 + R_4 + R_5
1/R_par = 1/R_145 + 1/R_3 R_par = (R_145 x R_3)/(R_45 + R_3) = [(R_1 + R_4 + R_5) x (R_3)]/(R_1 + R_4 + R_5 + R_3) = 8 Ohms
To the parallel part you need to add R_2 that is in series (with respect to the parallel part).
R_eq = R_2 + [(R_1 + R_4 + R_5) x (R_3)]/(R_1 + R_4 + R_5 + R_3) =
= R_2 + R_par = (4 + 8) Ohms = 12 Ohms c) You measure the current through R3 to be 12 Amps. What is the voltage of the battery? Show your work. if you consider the bottom parallel part you have Delta(V)_par = I_3 R_3 = 288 V
then you apply the same voltage to the upper parallel part (the voltage is the same in parallel circuits)
Delta(V)_par = I_145 (R_1 + R_4 + R_5)
which gives you I_145 = 288 V / 12 Ohms = 24 Amps
The total current is then I_tot = I_3 + I_145 = 36 Amps
Appling the ciruit equation to the whole circuit you get
E  I_tot R_eq = 0
then you plug in the R_eq from the previews question
E = I_tot R_eq = 36 Amps x 12 Ohms = 3 Volts d) The circuit to the right contains the same resistors and battery as the circuit above, but
the wires and resistors have been rearranged. Are the two circuits equivalent (same
currents through the battery and all resistors), or can you not tell with the given
information? C i r c l e you r c hoi c e b e l ow c l e a r l y . (No work needed).
R2 Equivalent Not Equivalent R3 R4 R5 Can't Tell (the shape is different but all the parallel series relations are the same) ! R1 ...
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 Spring '07
 JOHNCONWAY

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