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ECE 1250 Midterm 4 – Exam Topics: Capacitors and Inductors (Parts of Ch.5 and 7) You may also need to use the following concepts to solve the C and L problems: voltage /current dividers, KVL/KCL, Node-Voltage, impedances in series/parallel, Ohm’s Law. 1) Sinusoid Signal: Understand the terminology and find the values for a sinusoidal signal such as: amplitude, period, frequency, angular frequency, phase shift, and writing an expression for the sinusoid. Also ) understand the relationship between cosine and sin. ( ( ( )) 2) Capacitor and Inductor with a DC signal: a. Determine the model used for a capacitor and an inductor when a DC value is applied to them. b. Be able to analyze the circuit to determine either voltage across cap or current through inductor. c. Be able to write the general equation for the voltage (across cap) or current (through inductor). 3) Understand time constant: RC and RL circuits have exponential charge and discharge curves. For a given value of R and C or R and L in series, be able to sketch these curves, and write their equations. 63% at t=RC 37% at t=RC 63% at t=L/R 37% at t=L/R 4) Phasors. Be able to convert a sinusoidal equation to a phasor expression and vice versa. Be able to add, subtract, multiply, and divide phasors (using Matlab). 5) Impedances in Series and Parallel Be able to compute the impedance for any R,C,L. Be able to identify when impedances are in series and parallel. Be able to compute the total impedance of a set of impedances in series and/or parallel. 6) RLC circuits: Be able to write equations to find the voltages and / or currents in series and parallel RLC circuits. Be able to do this with the complex form of Ohm’s Law, voltage and/or current dividers, KVL/KCL, or node-voltage methods. I may suggest a method, but you can use any method that you prefer. I will NOT ask you to SOLVE these equations on this exam, just write them. You will also need to put them into matrix form. Examples (type 1) A sinusoidal voltage is shown below. 5 4 3 Current (A) 2 1 0 -1 -2 -3 -4 -5 0 0.1 0.2 0.3 0.4 0.5 0.6 time (sec) 0.7 0.8 Find: (a) A (amplitude) in Volts (V) (b) T (period) in seconds (c) f (frequency) in Hz (d) (angular frequency) in radians/sec (e) (phase shift) in radians or degrees (specify which unit you are using) (f) Write an expression for V in the time domain AND the phasor domain. 0.9 1 1.1 1.2 -3 x 10 Example (Type 2) . Switch open for a long time and then closed at t=0. a. Draw the appropriate model for the Initial time circuit for the capacitor. b. Analyze both the initial and the final circuit to determine the voltage across the capacitor c. Write the general equation for the voltage across the capacitor by first finding the time constant and then using answers from b. Original: Initial: Final: Example (Type 2) - Switch open for a long time and then closed at t=0. Leave answers in symbolic form. a. Draw the appropriate model for both the initial and final time for the inductor. b. Analyze both the initial and the final circuit to determine the current through the inductor c. Write the general equation for the current through the inducotr by first finding the time constant and then using answers from b. Original: Final: Example (Type 3) When the switch is closed at t=0, the voltage observed for the series RC circuit is shown below. a. Find an estimated value for C. b. Find the time constant from the above graph. c. What does the graph look like if C is increased in value? Example (Type 5) Write an expression for the equivalent impedance Zin. Use + to indicate ‘series’ elements and || to indicate parallel elements. Clearly indicate with () how to combine elements in the correct order. Be sure to specify the impedance for each element. Assume is given. Example (Type 6) Find the equations for each element (A11, A12, A21, A22, b1, b2) in the following matrix form for the circuit below. Assume is gven: [ ][ ] [ ] Example (Type 6) Use ( ). (a) Write the matrix in the following form: [ (b) Use Matlab to solve for , and Reference ][ ] Write ( ). [ ]