Chapter 13 The Math for Graphing in DC Circuits

Graphing Overview  Critical for practical analysis many different natural systems. Note: Theoretical analysis involves using mathematical models and describing equations. Practical analysis of electronic circuits and devices o Build the circuit, control variables, measure and record results o Plot results  Example Diode Voltage/Current characteristics o Test Circuit 13-1 on page 271  Change voltage across diode in steps  Record current through Plot data on X-Y coordinate grid Fig 13-3a Sometimes you plot on Log paper Fig 13-3b

Graphing Overview  Semi-Log paper

Graphing Plotting data on a system of rectangular coordinates  See Figure 13-4 for key points Horizontal and vertical axes o Can have different scales o Horizontal axis is often called the X Axis o Vertical axis is often called the Y Axis Point were they cross is the origin o Both are number lines with their zeros at the origin Identifying points on the graph o Points are given x and y values/coordinates o Example: Point __ (X, Y)  With numbers Point A (5, -2) & Point B (-4, 6)  See Figure 13-5 on page 273 and next slide o Practice Problems – top of page 274

Graphing Plotting data on a system of rectangular coordinates

Graphing Graphing Linear Equations  Review of Linear Equations Terms only one variable o Multi-term expressions or equations may have different variables Variable exponent =1 Examples o 2x + 1 = 9 o 5 + 6a = 23 o 6x + 7y = 14  A graph of a Linear Equation is a straight line Example: 2x – y = 6 o If y = 0  2x =6  x = 3 Point (3, 0) o If x = 0  y = -6 Point (0, -6)

Graphing Graphing Linear Equations  A graph of a Linear Equation is a straight line Example: 2x – y = 6 o Plot those points o Draw a straight line through them o You have plotted the linear equation Work through Example 13-1 on page 276 Work through some practice problems on page 276

Graphing Do Example 13-2 on page 278 Work Practice problems on page 278

Graphing

Interpreting Graphs  Time Constant Plot for simple R & C circuit (page 282) Do Example problems 13-4 and 13-5 on page 282 Practice Problems on page 13-5 Plotting Curves  Critical to determine the independent variable and the dependent variable For example in Fig (page 280) o Changes in V result in new values for I o Independent variable is usually plotted with respect to the X Axis o The resulting dependent values are plotted with respect to the y Axis

Graphing Plotting Curves  Example Problem 13-6

Graphing Plotting Curves  Example Problem 13-7