EE1305/EE1105 Homework Problems Packet P1 - The gate length of a tri-gate transistor is 22 nm. How many gate lengths fit across a human hair with a diameter of 100 μm? Show all units and unit conversions for each of your calculations. P2 - Determine the kinetic energy (in ev) of an electron traveling at a velocity of 9 x 10 6 m/s if the kinetic energy of the electron is equal to ½ mv 2. Show all units and unit conversions for each of your calculations. P3 - An electron has charge, q, equal to 1.6 x 10-19 coulombs (C), and is experiencing an electric field equal to 5 x 10 11 V/cm. (a) Calculate the force on the charge using E = F/q, where E is the electric field and F is the force on the charge. (b) Calculate the work (in units of ev) done on the charge if the charge is accelerated a distance of 1 cm. Use the equation W = F x d, where W is the work done on the charge, d is the distance the charge is moved, and F is the force on the charge. Use the following unit conversions: 1.6 x 10-19 J = 1 ev, 1 V = 1 J/C and 1 J = 1 N m. Show all units and unit conversions for each of your calculations. P4 - The current flowing through three resistors in series (R1, R2 and R3) is 7.69 ma. Since the three resistors are in series, the current flowing through each resistor is the same. (a) Use Ohm s Law to determine the voltage drop across each resistor. (b) Add the voltage drop across each resistor. Show all units and unit conversions for each of your calculations. P5: Compare the resistance of a 1 m wire with a radius of 1.3 mm for each of the following materials: Copper Gold Show all units and unit conversions in your calculations.
P6. Prove that the equation relating change in potential energy to voltage is dimensionally consistent, using the unit conversions provided below. V = P. E. q V change in Voltage (units V) P. E. change in Potential Energy (units ev) q Electron Charge equal to 1.6 x 10 19 C P7. Calculate the equivalent resistance for the resistors in series. Use the equivalent resistance to determine the current flowing through each resistor. Make sure to show the unit conversion V = A when setting up your current (I) calculation. Show all units and unit conversions for each calculation. 1 k Unit Conversions: 1.6 x 10 19 J = 1 ev V = J/C 2 k 1.5 k P8. The circuit below includes 3 resistors in parallel, R1 = 1 k, R2 = 2 k, and R3 = 4k. (a) Determine the equivalent resistance (Req), (b) use Ohm s Law to determine the circuit current, and (c) use Ohm s law to determine the current through each resistor. 10 V
P9. (a) Use the shorthand notation/equivalent circuit method to reduce the circuit until there are only 2 resistors left. For each step, show the equivalent circuit, and write the shorthand notation expression. (b) When there are only 2 resistors left, determine the expression for the voltage drop at VA using the voltage divider method. Make sure to include the equation for voltage divider at the beginning of this step. VA P10. (a) Determine the circuit current for the simplified circuit in P9 if R1 R4 are equal to 100 and Vin is equal to 9 V, (b) Use Ohm s Law to confirm the voltage drop at VA, and (c) Use the expression for P9 part (b) to determine VA using the voltage divider method. Show every step, units, and unit conversions for full credit. P11. (a) Determine the voltages at nodes A, B, C and D. (b) Determine the currents I1 I7. (c) Determine the power generated or consumed by each component, and (d) Determine if conservation of power exists in this circuit. Label each step and include units and unit conversions for full credit. P12. (a) Simplify the circuit and determine the equivalent resistance. (b) Determine the circuit current, and (c) Determine the power consumed by the equivalent resistance and the power supplied by the 12 V source. (d) Does conservation of power exist in the circuit? Label each step and include units and unit conversions for full credit.
VA P13. (a) Simplify the circuit in P12 in order to, (b) use Voltage Divider to determine the value of VA, and (c) use Ohm s Law to calculate the current through the 5 k resistor. P14. Use any method to (a) determine the voltage drop across the 6 k resistor, (b) the current flowing through it, and (c) the power consumed by the 6 k resistor. P15. (a) Determine the cut-off frequency for the low-pass filter shown below. Include all units and unit conversions for full credit. (b) If a signal frequency is increased to 10 khz, will its amplitude be diminished or will it remain intact as it is processed by the filter?
P16. Assume that the circuit below has reached equilibrium and that the capacitor is fully charged. (a) Determine the value of VA, (b) the current flowing through R1, R2 and R3, and (c) the power consumed by R3. Show all equations required to solve this problem, all units, and all unit conversions for full credit. VA R1 R2 R3 P17. ( a) Write the expression for KVL for the circuit below, and (b) determine the value of the current (I). I P18. Use KCL and KVL to solve for I1, I2 and I3, and then use Ohm s Law to determine the voltage across the 10 k resistors at Node A. Assume that the current is flowing in the directions indicated in the circuit diagram below. A I1 I3 I2
P19. (a) Use KCL and KVL to solve for I1, I2 and I3, assuming that the current is flowing in the directions indicated by the current arrows in the circuit diagram below, and then (b) re-sketch the circuit with the correct current directions based on your KCL/KVL analysis. I1 I3 I2 P20. (a) Use KCL and KVL to solve for I1, I2 and I3, assuming that the current is flowing in the directions indicated by the current arrows in the circuit diagram below, and then (b) re-sketch the circuit with the correct current directions based on your KCL/KVL analysis. Assume that the circuit has reached equilibrium and that the capacitor is fully charged. (c) re-work the problem if the 8 V power supply is replaced with a 6 V power supply. I1 I3 I2 P21. Use KCL at node A to develop an expression for Vout in terms of Vin, R1 and R2. Use the same approach used for the inverting amplifier example explained in class.
R P22. (a) Calculate the cut-off frequency (fc) for an active filter with R = 10 k and C = 10 F, and (b) Plot the expression for V OUT = R 2 1 in MATLAB, where j is the imaginary number V IN R 1 1+jωR 2 C equal to ( 1), ω is angular frequency equal to 2πf, f is frequency, R is resistance and C is capacitance. This expression will generate a Bode Plot illustrating the behavior of an active filter with 2 resistors and 1 capacitor. To plot in MATLAB, type in the following commands, and specify whether the filter is low-pass or high-pass. >> w=logspace(-3,5,100); y = logspace(a,b,n) generates n=100 points between decades 10-3 and 10 5 >> j=sqrt(-1); >> R1=1E3; >> R2=10E3; >> R2=10E3; >> C=10E-6; >> Vout=(-R2/R1)*1./(1+j*w*R2*C); the. / is used for mathematical operations for matrices >> loglog(w/2/pi, abs(vout)) creates a loglog plot of w vs Vout by converting w in radians/sec to f in Hz since w = 2f or f = w/2 Add the x-axis and y-axis labels, and label the fc value, and print a copy to turn in with your homework. P23. Use Complex Impedance and KCL to prove that the expression for Vout/Vin for the passive low pass filter shown below is equal to... V out V in = jwcr jwcr + 1 C Vin Vout Show all steps. P24. Graph Vout/Vin in MATLAB for P23. Use the MATLAB code included in P22 to guide you.