Solution of Final Exam Problems 1

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1 of Final Exam Problems Prob. Two different electrical devices have the same power consumption, but one is meant to be operated on 20 V AC and the other on 220 V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 20 V AC device is connected to 220 V AC? (a) (b) P V 2 R V 2 V 2 2 R R 2 ( R 2 V2 R V ( ) 2 ) 2 (c) P IR 2 I2R 2 2 I 2 I (R ) R 2 ( ) P V 2 R

2 of Final Exam Problems 2 P 2 V 2 2 P V 2 ( ) 2

3 of Final Exam Problems 3 Prob. 2 (a) What is the potential difference going from point a to point b in Figure ()? 20.0 cm B out I Figure : Circuit diagram. (b) What is the potential difference going from c to b? (c) From e to g? (d) From c to d? In order to get the various potential difference we need to find the three current flowing in the circuit. We have three unknowns, so we need three equations. Applying Kirchhoff s rules to the current junction at b and clockwise on abcdef a loop and abefa loop we get: I I 2 + I 3 ()

4 of Final Exam Problems 4 0 I R I 2 R 3 + E 3 I 2 r 3 I 2 r 4 E 4 I R 4 + E I r (2) 0 I R I 3 R 2 + E 2 I 3 r 2 I R 4 + E I R (3) Rearranging Equation (2) and Equation (3) we get: 0 I (R + r + R 4 ) I 2 (R 3 + r 3 + r 4 ) + (E + E 3 E 4 ) (4) 0 I (R + r + R 4 ) I 3 (R 2 + r 2 ) + (E + E 2 ) (5) Plugging in the numbers we get: I 9.25I (6) I 6.25I (7) Substitution for I from Equation () in Equation (6) and Equation (7) we get: Using Equation (8) we get: I I (8) I I (9) I I 2 (0) 35.5 Substituting for I 3 from Equation (0) into Equation (9) we get: 2 [ ] I I I A () Substituting for I 3 from Equation () into Equation (0) we get: I A (2) Finally, substituting for I 2 from Equation () and I 3 from Equation (2) into Equation () we get: I I 2 + I A We can now calculate the required potential differences.

5 of Final Exam Problems 5 (a) (b) V ab I R V (c) V cb I 2 R V (d) V eg E 2 I 3 r V V ed E 4 + I 2 r V

6 of Final Exam Problems 6 Prob. 3 The force on the rectangular loop of wire in the magnetic field shown in Figure (2) can be used to measure field strength. The field is uniform, and the loop is perpendicular to the field cm B out I Figure 2: A rectangular loop of wire carrying a current is perpendicular to a magnetic field. The field is uniform in the region shown and is zero outside that region. (a) What is the direction of the magnetic force on the loop? What is the direction of the net magnetic force on the loop? Does the magnetic force on the sides of the loop affect the net magnetic force on the loop? Explain your answer. (b) If a current of 5.00 A is used, what is the force per tesla on the 20.0 cm wide loop?

7 of Final Exam Problems 7 (a) The net force is down the page. NO, the magnetic force on the sides does not affect the net magnetic force on the loop. The reason is that I, l, B, and θ are the same for each side. The Right Hand Rule indicates that the two forces are in opposite directions and along the sam line. So, they cancel out. (b) F B Il N/T

8 of Final Exam Problems 8 Prob. 4 An image of a flower is produced on a screen by a lens.60 m from the screen. The image of the flower has a linear magnification of 2.5. What is the focal length of the lens? The magnification of the lens is given by: so the object distance is: m i o Using the the lens formula we get: o i m i m f o + i f oi o + i i m i m i 2 i + m i i + m m

9 of Final Exam Problems 9 Prob. 5 A 200-turn flat coil of wire 30.0 cm in diameter acts as an antenna for F M radio at a frequency of 00 M Hz. The magnetic field of the incoming electromagnetic wave is perpendicular to the coil and has a maximum strength of T. (a) What power is incident on the coil? (b) What average emf is induced in the coil over one-fourth of a cycle? (c) If the radio receiver has an inductance of 2.50 µh, what capacitance must it have to resonate at 00 MHz? (a) P IA ( ) cb 2 (πr 2 ) 2µ [ ] [π ( ) 2] 2(4π 0 7 ) W (b) t T 4 4f s E N Φ t NA B t Nπr2 B t

10 of Final Exam Problems 0 (c) 200π ( ) V f 2π LC C 4π 2 Lf 2 4π ( ) F

11 of Final Exam Problems Prob. 6 A camera with a 00 mm focal length lens is used to photograph far away objects like the sun and the moon. What is the height of the image of the sun on the film, given the sun is km in diameter and is km away? + d d i f ( d i f ) d (/f) (/d ) d i d (d /f) (.5 0 / ) h i h h i h mm

12 of Final Exam Problems 2 Prob. 7 The spectral series corresponding to n 4 in hydrogen is called the Brackett series. What are the longest and shortest wavelengths in the Brackett series? The wavelengths of hydrogen spectral lines are given by: ( λ R ) n n 2 n 2 < n 2 2 where R m is Rydberg constant. For Brackett series n 4 and n 2 5, 6, 7,. So, the longest wavelength λ L comes from n 4 and n 2 5 transition, while the shortest wavelength comes from n 4 and n 2 transition, we then have: ( R λ L 6 ) 25 ( ) 25 6 R 25 6 λ L 25 6 R m m 405 nm ( R λ s 6 λ s 6 R ) m m 459 nm

13 of Final Exam Problems 3 Prob. 8 Monochromatic light is incident on two narrow slits whose separation is mm. An interference pattern forms on a screen 90.0 cm away. If adjacent interference maxima are separated by.06 mm, what is the wavelength of the light. Let y and y 2 be the position of the first (m ) and second (m 2) maxima from the center. We then have: mλ d sin θ where d is the width of each slit and sin θ y/l where L is the distance to the screen. λ d y L 2λ d y 2 L y 2 y 2Lλ d Lλ d Lλ d λ d(y 2 y ) L m m 589 nm

14 of Final Exam Problems 4 Prob. 9 Calculate the voltage across the 20 µf capacitor in the circuit of Figure (3). The battery voltage is 9.0 V. 0 µf 9.0 V 0 µf 20 µf Figure 3: The voltage across the the series combination of the 0 µf and the 20 µf capacitors is 9.0 V. The series equivalent of these two capacitors is: C + C c 2 C C C 2 C + C µf The charge Q on the series equivalent is the same as the charge on each capacitor and given by: Q CV µc

15 of Final Exam Problems 5 The voltage across the 20.0 µf capacitor is given by: V Q C V

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