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F 07 314 ex1 all-s

# F 07 314 ex1 all-s - EECS 314 Problem 1 Fall 2007 Exam 1...

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EECS 314 Fall 2007 Exam 1 Instructor: Alexander Ganago Problem 1 In the circuit shown on this diagram, the source voltage, the output voltage, and resistance R are known. Which formula should be used to calculate the unknown resistance RX ? A. RX = R " VS # VOUT VOUT B. RX = R # VOUT VS + VOUT C. RX = R " VS # VOUT VS D. RX = R " VOUT VS # VOUT E. RX = R # VS VS + VOUT Solution According to voltage division, VOUT = VS # RX R + RX Thus, VOUT # R + RX () = VS # RX , and VOUT " R = RX " VS # VOUT Eventual y, RX = R " VOUT VS # VOUT , which matches formula D. Answer: D EECS 314 Fall 2007 Exam 1 Instructor: Alexander Ganago Problem 2 In the circuit shown on this diagram, the cur ent source absorbs … A. 36 W B. 12 W C. Zero D. – 12 W E. – 36 W Solution According to KCL, the same cur ent flows through al elements of this circuit. The reference marks on this diagram are chosen according to the Passive Sign Convention so that the cur ent enters the more positive terminal of the resistor and the cur ent source. Note that the cur ent exits the positive terminal of the voltage source, which means that this source supplies power. According to KVL, # 12 V + VR + VX = 0 According to Ohm’s law, VR = 2 A ()" 3 # () = 6 V Thus, VX = V The power absorbed by the cur ent source equals P A = V # A 12 W Answer: B Note that the power balance holds: the voltage source supplies power, or absorbs P 12 V = 12 V ()"# A ()=# 24 W (the negative sign indicates that the cur ent enters the negative terminal of the source) The resistor absorbs PR = A 2 " # 12 W The power balance is P 12 V + PR + P A =# 24 W + 12 W + 12 W = 0 as expected. Calculation of the power balance is not required but helps to reassure oneself that the result is cor ect. EECS 314 Fall 2007 Exam 1 Instructor: Alexander Ganago Problem 3 With the wire (zero resistance) connected to the terminals A and D, the equivalent resistance between terminals B and C is… A. R B. 1.75 # R C. 2.875 # R D. 3.1 # R E. 4 # R Solution For the sake of clarity, we can redraw the circuit. When voltage is applied between terminals B and C in order to measure the equivalent resistance, the cur ent does not flow through the 2 # R resistor because it flows through the wire instead. Thus we can delete the 2 # R resistor from the equivalent diagram, as shown below. Thus, connected to terminal C is a paral el combination of (3 # R) and (R + 4 # R), which is connected in series with R. The bot om diagram shows the equivalent circuit, for which the calculation is straightforward: RBC = R + (3 # R ) # (4 # R + R ) (3 # R ) + (4 # R + R ) = = 1 + 15 8 " ! ± ² ³ ´ # R = = 2.875 # R Answer: C EECS 314 Fall 2007 Exam 1 Instructor: Alexander Ganago Problem 4 The circuit shown on this diagram was used in experiments with MOSFET in which the supply voltage V dd = +6 V is constant, the VGS voltage is varied, and the VDS voltage is measured.

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F 07 314 ex1 all-s - EECS 314 Problem 1 Fall 2007 Exam 1...

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