Name: PHYS122 Hourly Exam 2 1. A charge Q1 = −48 × 10-6 coulomb is fixed on the x-axis at +4.0 meters, and a charge Q2 = +18 × 10-6 coulomb is fixed on the y-axis at +3.0 meters, as shown in the dia-gram above. (a) i. Calculate the magnitude of the electric field E1 at the origin due to charge Q1. ii. Calculate the magnitude of the electric field E2 at the origin due to charge Q2. −48 × 10-6 C Q1 x (m) y (m) Q2 +18 × 10-6PHYS122 Exam 2 -2- iii. On the axes below, draw and label vectors to show the electric fields E1 and E2 due to each charge, and also indicate the resultant electric field E at the origin. (b) Calculate the electric potential V at the origin A charge Q3 = −5 × 10-6 coulomb is brought from a very distant point by an external force and placed at the origin. (c) On the axes below, indicate the direction of the force on Q3 at the origin.PHYS122 Exam 2 -3- (d) Calculate the work that had to be done by the external force to bring Q3 to the origin from the distant point. 2. Robert Millikan received the Nobel Prize for determining the charge on the electron. To do this, he set up a potential difference between two horizontal parallel metal plates. He then sprayed drops of oil between the plates and adjusted the potential dif-ference until drops of a certain size remained suspended at rest between the plates, as shown above. Suppose that when the potential difference between the plates is ad-justed until the electric field is 106 N/C downward, a certain drop with a mass of 6.54 × 10-13 kg remains suspended. (a) What is the magnitude of charge on this drop? (b) The electric field is downward, but the electric force on the drop is upward. Explain why. (c) If the difference between the plates is 0.0001 m, what is the potential differ-ence between the plates? •PHYS122 Exam 2 -4- (d) The oil drop slowly evaporates while the drop is being observed, but the charge on the drop remains the same. Indicate whether the drop remains at rest, moves upward, or moves downward. Explain briefly. 3. The circuit shown above includes a switch S, which can be closed to connect the 3-microfarad capacitor in parallel with the 10-ohm resistor or opened to disconnect the capacitor from the circuit. Case I. Switch S is open. The capacitor is not connected. Under these conditions determine: (a) the current in the battery (b) the current in the 10-ohm resistor (c) the potential difference across the 10-ohm resistor.PHYS122 Exam 2 -5- Case II. Switch S is closed. The capacitor is connected. After some time, the cur-rents reach constant values. Under these conditions determine: (d) the charge on the capacitor (e) the energy stored in the capacitor. 4. A student is provided with a 12-V battery of negligible internal resistance and four resistors with the following resistances: 100 Ω, 30 Ω, 20 Ω, and 10 Ω. The student al-so has plenty of wire of negligible resistance available to make connections as desired. (a) Using all of these components, draw a circuit diagram in which each resistor has nonzero current flowing through it, but in which the current from the bat-tery is as small as possible.PHYS122 Exam 2 -6- (b) Using all of these components, draw a circuit diagram in which each resistor has nonzero current flowing through it, but in which the current from the bat-tery is as large as possible..PHYS122 Exam 2 -7- The battery and resistors are now connected in the circuit shown above. (c) Determine the following for this circuit. i. The current in the 10-Ω resistor ii. The total power consumption of the circuit. (d) Assuming that the current remains constant, how long will it take to provide 10 kJ of electrical energy to the circuit?PHYS122 Exam 2 -8- 5. A certain light bulb is designed to dissipate 6 watts when it is connected to a 12-volt source. (a) Calculate the resistance of the light bulb. (b) If the light bulb functions as designed and is lit continuously for 30 days, how much energy is used? The 6-watt, 12-volt light bulb is connected in a circuit with a 1500-watt, 120-volt toaster; an adjustable resistor; and a 120-volt power supply. The circuit is designed such that the bulb and the toaster operate at the given values and, if the light bulb fails, the toaster will still function at these values. (c) On the diagram below, draw in wires connecting the components shown to make a complete circuit that will function as described above. (d) Determine the value of the adjustable resistor that must be used in order for the circuit to work as designed.PHYS122 Exam 2 -9- (e) If the resistance of the adjustable resistor is increased, what will happen to the following? i. The brightness of the bulb. Briefly explain your reasoning. ii. The power dissipated by the toaster. Briefly explain your reasoning.PHYS122 Exam 2 -10- Equations 122EKqqFr= 29201Nm8.99 104CKπε==×271.67 10 kgpm−=× onqFEq→=r 2014qErπε= 0QEAε= 191.6 10 Ce−=× 319.11 10 kgem−=× 21202C8.85 10Nmε−=× EUqV= 12 12014Eqq qqUKrrπε== 014qqVKrrπε== VEdΔ= QCV=Δ 0ACdκε= ()221122CQUCVC==Δ QItΔ=Δ VIRΔ= LRAρ= WPIVt==Δ in outII=∑∑ 0loop iiVVΔ=Δ=∑ 12sNRRR R=+++K 12pNCCC C=+++K 12111 1pNRRR R=+++K 12111 1sNCCC C=+++K 111oifdd=+
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