Question = A sawtooth signal u has the form u(t) = at/T for 0 <t<T, and is T-periodic (i.e., repeats every T seconds). The constant a is called the amplitude of the signal, and the constant T (which is positive) is called the period of the signal. You can assume that a > 0. a a (a) Find the peak value of a sawtooth signal. (b) Find the RMS (root-mean-square) value of a sawtooth signal. (c) Find the AA (average-absolute) value of a sawtooth signal. (d) In the space below, sketch the derivative of a sawtooth signal. Be sure to label all axes, slopes, magnitudes of any impulses, etc.

1-5 Measure the voltage across the capacitor, V Record this voltage in the 19-2. Theme ct Two ITE na of yo ubject the 3 dos voltage to compete the capacitive reactance using Ohm's luw X - 2Afc - Enter this value as the capacitive reactance in Table 19-2. (2X* X 29 = 1823.12 Using the capacitive reactance found in step 4. compute the capacitance using the equation 2nX125370 Enter the computed capacitance in Table 19-2. This valuesfuld agree with the value markede the capacitor and measured in step within experimental torces Repeat steps 3, 4 and 5 using capacitor Center the data in Table 19-2 in the column labeled Capacitor C 1 250x Oo87 6. 7. Now connect in series with C. The equivalent capacitive reactance and capacitance can be found for the series connection by measuring across both capacitors as if they were one capacitor Enter the data in Table 19-3 in the column labeled Series Capacitors. The following steps will guide you (a) Check that the generator is set to 1.0 Vrms. Find the current in the circuit by measuring the voltage across the resistor as before and dividing by the resistance. Enter the measured voltage and the current you found in Table 19-3. (b) Mensure the voltage across both capacitors. Enter this voltage in Table 19-3. (c) Use Ohm's law to find the capacitive reactance of both capacitors. Use the voltage measured in step (b) and the current measured in step (a). (d) Compute the total capacitance by using the equation Va Ves 1 C- 2X Connect the capacitors in parallel and repeat step 7. Assume the parallel capacitors are one equivalent capacitor for the measurements. Enter the data in Table 19-3 in the column labe ! Parallel Capacitors. Table 19-3 Step (a) Series Parallel Capacitors Capacitors Voltage across R. V 0.29 V 0787 Tocal current, 0.19 078.AL Voltage across capacitors, Vc S 0.62V> Capacitive reactance, Xa A31947 25194.12 Computed capacitance, beruf 0.207 (b) d 159 an you saw in As your group and process chart andre Observation. When 1 rok se CONCLUSION description de the needed cal nderstan EVALUATION AND REVIEW QUESTIONS Compare the capacitive reactance of the series capacitors with the capacitive reactance of the parallel capacitors. Use your data in Table 19-3 pue 2. Compare the total capacitance of the series capacitors with the total capacitance of the parallel capacitors 3. If someone had mistakenly used too small a capacitor in a circuit, what would happen to the capacitive reactance? 4 How could you apply the method used in this experiment to find the value of the unknown capacitor? 5. Compute the capacitive reactance for an 800 pF capacitor at a frequency of 250 kHz. 160

R W R3 ww 10 12 ww R2 1 Write down the Kirchhoff Junction equation and solve it for I; in terms of 12 and 13. Write the result here: Ij = write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and follows the perimeter of the circuit diagram clockwise. 0 write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and touches the components 10V, Ry, 4V, and Ry O The resistors in the circuit have the following values . - R2 • Ry=60 Ry=130 Solve for all the following (some answers may be negative); 11 - Amperes 12 Amperes 13 Amperes NOTE: Forthin

3. Find the area between the curve y = 2^x andthe chord joining the points (0,1) and (2,4). 4. Find the coordinates of the centroid bounded bythe curve y = x^3 and the line x = 2.

16. A disk, a hoop and a solid sphere are released at the same time at the top of an inclined plane. They all roll without slipping. In what order do they reach the bottom? a. Disk, hoop, sphere b. Hoop, sphere, disk c. Sphere, disk, hoop d. Sphere, hoop, disk e. Hoop, disk, sphere 17. A wheel rotates through an angle of 360° as it slows down from 78 rpm to 16. A disk, a hoop and a solid sphere are released at the same time at the top of an inclined plane. They all roll without slipping. In what order do they reach the bottom? a. Disk, hoop, sphere b. Hoop, sphere, disk c. Sphere, disk, hoop d. Sphere, hoop, disk e. Hoop, disk, sphere 17. A wheel rotates through an angle of 360° as it slows down from 78 rpm to 2 What is the magnitude of the average angular acceleration of the wheel?! a 8.14 rad/s

Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set of al 4 x 4 matrices of the form O b a a o b c са о babi with the standard operations O The set is a vector space. O The set is not a vector space because it is not closed under addition. O The set is not a vector space because it does not satisfy the associative property of addition. O The set is not a vector space because a scalar identity does not exist. O The set is not a vector space because it does not satisfy the distributive property.

2. B) A 600-kg car traveling at 24.5 m/s is going around a curve having a radius of 120 m that is banked at an angle of 20.0 degrees. Is the curve properly banked for the car's speed? Explain. A yes or no answer is not enough. Show your work to support your answer. 2.88 M - Goo МА .600 x 987 MS = 600 X 24,5 2. B) A 600-kg car traveling at 24.5 m/s is going around a curve having a radius of 120 m that is banked at an angle of 20.0 degrees. Is the curve properly banked for the car's speed? Explain. A yes or no answer is not enough. Show your work to support your answer. 2.88 M - Goo МА .600 x 987 MS = 600 X 24,5