How much lag?If you know the ratio of the inductive reactance to the resistance, XL/R, in an RL circuit,then you can find the phase angle. Of course, you can find the angle of lag if you knowthe actual values of XL and R.Pictorial methodIt isn’t necessary to construct an entire RL plane to find phase angles. You can use aruler that has centimeter (cm) and millimeter (mm) markings, and a protractor.First, draw a line a little more than 10 cm long, going from left to right on a sheetof paper. Use the ruler and a sharp pencil. Then, with the protractor, construct a lineoff the left end of this first line, going vertically upwards. Make this line at least 10cm long.The horizontal line, or the one going to the right, is the R axis of a crude coordinatesystem. The vertical line, or the one going upwards, is the XL axis.If you know the values of XL and R, divide them down, or multiply them up (in yourhead) so that they’re both between 0 and 100. For example, if XL680Ω and R840Ω, you can divide them both by 10 to get XL68 and R84. Plot these points lightlyby making hash marks on the vertical and horizontal lines you’ve drawn. The R markwill be 84 mm to the right of the origin, or intersection of the original two perpendicu-lar lines. The XL mark will be 68 mm up from the origin.Draw a line connecting the two hash marks, as shown in Fig. 13-12. This line willrun at a slant, and will form a triangle along with the two axes. Your hash marks, and theorigin of the coordinate system, form vertices of a right triangle. The triangle is called“right” because one of its angles is a right angle (90 degrees.)240 Inductive reactance13-11In a circuit with only resistance, the current is in phase with the voltage.