12. A voltage difference V is applied between the two inputs V₁ and V₂ in the circuit diagram below.  The  capacitors have the following  values: C₁=5.0 pF, C₂=4.0 pF, and C₃=8.0 pF. The voltage  relationships between the points are defined as: =V₁-V₂, =V₂-V₃, and=V₁-V₃. Calculate the amount of charge Q₃ in pC unit when =180 V.

(A) 884
(B) 960
(C) 1016
(D) 1145
(E) None of the above.

11. In an LC oscillating circuit, the initial energy is stored entirely in the capacitor, which is fully charged to a maximum charge Q = 2 µC. The circuit has: Capacitance C= 5 µF, Inductance L = 0.1 H. The charge q on the capacitor when the energy in the electric field is one-third of the energy in the magnetic field. Please find that the time required to reach this condition, expressed in terms of the oscillation period T. (A) T/2 (B) T/3 (C) T/4 (D) T/5 (E) T/6

13. As shown in the right figure, take &0 = 24 V, R1 =6.0 , R2 = 12, and R3 = 3.0Ω. Write the current I1 for a long time after the switch is closed. (A) 1.7 A (B) 2.9 A (C) 3.7 A (D) 4.3 A (E) 5.5 A R3

14. Consider an RLC series circuit with a resistor R=100 , an inductor L=0.2 H, and a capacitor C=50 µF, connected to a sinusoidal voltage source V(t)=V0cos(ωt) with V0=10 V. Using the phasor method, find the resonant frequency of the circuit. (A) 21.5Hz (B) 32.8Hz (C) 40.6Hz (D) 50.3Hz (E) 62.7Hz

15. A solenoid is wound with 1200 turns on5.0 cm ↓ a cylindrical form 5.0 cm in diameter and 60 cm long. The windings carry a current I in the direction shown in the diagram. The current produces a magnetic field of magnitude 5.2 mT near the center of the solenoid. Calculate the current I in the solenoid windings. Use T m/A. (A) 1.69 A (B) 2.07 A (C) 3.64 A (D) 4.02 A (E) 5.53 A U

16. You're designing a spectrometer that needs a minimum angular separation of Omin = 6° between the second-order (m = 2) lines of hydrogen (Ha) at 656 nm and potassium (K) at 769 nm. What is the line spacing d for an optical grating that can achieve the required angular separation? (A) 2.159 µm (B) 3.302 µm (C) 4.473 um above. (D) 5.589 µm (E) None of the

17. In a Michelson interferometer, one arm is 55.0 cm long and is enclosed in a box that can be evacuated. Initially, the box contains air, which is gradually pumped out, causing a change in the optical path length in that arm. During the evacuation process, 520 bright fringes pass by a point in the viewer. The interferometer uses light with a wavelength of 600 nm. What is the refractive index of air? (A) 1.000293 (B) 1.000162 (C) 1.000096 (D) 1.00028 (E) 1.00006

18. In a double-slit experiment, the wavelength λ of the light source is 520 nm, the slit separation d is 25 µm, and the slit width a is 5 µm. Consider both the interference of the light from the two slits and the diffraction of the light through each slit. How many bright interference fringes are within the central peak of the diffraction envelope? (A) 9 (B) 10 (C) 11 (D) 12 (E) 13

19. An electric field points into the page and occupies a circular region of radius 1.5 m, as shown in the right figure. There are no electric charges in the region, but a magnetic field forms closed loops pointing counterclockwise around the electric field region. The magnetic field strength 1.0 m from the center of the region is 2.5 µТ. What's the rate of change of the electric field? (A)(B) (C)(D) (E) 

20. A laser beam reads information from a compact disc with an initial diameter of1.900 mm as it strikes the disc. The laser forms a cone with a half-angle θ1=30.0° (as shown in the figure). The beam then passes through a 1.50 mm thick layer of plastic with a refractive index of 1.60 before reaching the reflective information layer near the disc's top surface. What's the beam diameter d at the information layer?  (A) 726 µm (B) 846 µm (C) 914 µm (D) 1056 µm (E) 1168 µm

1. The wave function of a transverse wave propagating on a rope is given by: y(x,t)=4 sin(0.5x+30t), where x and y are measured in meters, and t is in seconds. Find the velocity of a particle on the rope at x = 2 m and t = 0.4 s. (A) 100.52 m/s (B) 108.84 m/s (C) 116.88 m/s (D) 124.19 m/s (E) None of the above.

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