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Pure Resistance As the resistance in an RC circuit gets large compared with the absolute value of the capacitive reactance, the angle of lead becomes smaller The same thing happens if the absolute value of X C gets small compared with the value of R When R is many times larger than the absolute value of X C , whatever their actual values, the vector in the RC plane points almost along the R axis Then the RC phase angle is close to 0 The voltage comes nearly into phase with the current The plates of the capacitor do not come anywhere near getting fully charged with each cycle The capacitor is said to pass the ac with very little loss, as if it were shorted out But it will still have an extremely high X C for any ac signals at much lower frequencies that might exist across it at the same time (This property of capacitors can be put to use in electronic circuits An example is when an engineer wants to let radio-frequency signals get through while blocking signals at audio frequencies) Ultimately, if the absolute value of the capacitive reactance gets small enough, the circuit acts as a pure resistance, and the current is in phase with the voltage

var loopIndex = 0; while(students[loopIndex] != "Nancy" && loopIndex < studentslength - 1){ loopIndex++; }

The expression studentslength returns the number of total elements in the array, so setting up the while loop this way makes it loop until loopIndex is incremented to studentslength 1, or 7, unless Nancy is found at an earlier index If, at the end of this while loop, the variable loopIndex is less than or equal to the index of the last element in the array (which is studentslength 1), then we found Nancy, and we can report that fact this way (in whilehtml):

If you know the ratio of capacitive reactance to resistance, or XC /R, in an RC circuit, then you can find the phase angle Of course, you can find this angle if you know the precise values, too

<html> <head> <title>Using the while loop</title> <script language="javascript"> function display() { var loopIndex = 0, students = new Array(6); students[0] students[1] students[2] students[3] students[4] students[5] students[6] students[7] = = = = = = = = "George"; "Ed"; "Stella"; "Ted"; "Liz"; "Cary"; "Nancy"; "Zack";

Pictorial Method You can use a protractor and a ruler to find phase angles for RC circuits, just as you did with RL circuits in the previous chapter, as long as the angles aren t too close to 0 or 90 First, draw a line somewhat longer than 10 cm, going from left to right on the paper Then, use the protractor to construct a line going somewhat more than 10 cm vertically downward, starting at the left end of the horizontal line The horizontal line is the R axis of an RC plane The line going down is the X C axis If you know the actual values of X C and R, divide or multiply them by a constant, chosen to make both values fall between 100 and 100 For example, if X C = 3800 and R = 7400 , divide them both by 100, getting 38 and 74 Plot these points on the lines The X C point goes 38 mm down from the intersection point between your two axes The R point goes 74 mm to the right of the intersection point Next, draw a line connecting the two points, as shown in Fig 14-11 This line will be at a slant and will form a triangle along with the two axes This is a right triangle, with the right angle at the origin of the RC plane Measure the angle between the slanted line and the R axis Use the protractor for this Extend the lines, if necessary, using the ruler, to get a good reading

while(students[loopIndex] != "Nancy" && loopIndex < studentslength - 1){ loopIndex++; }

on the protractor This angle will be between 0 and 90 Multiply this reading by 1 to get the RC phase angle That is, if the protractor shows 27 , the RC phase angle is 27 The actual vector is found by constructing a rectangle using the origin and your two points, making new perpendicular lines to complete the figure The vector is the diagonal of this rectangle, running out from the origin (Fig 14-12) The phase angle is the angle between the R axis and this vector, multiplied by 1 It will have the same measure as the angle of the slanted line you constructed in Fig 14-11

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if(loopIndex <= studentslength - 1){ documentgetElementById('targetDiv')innerHTML = "I found Nancy at student location " + loopIndex; } else { documentgetElementById('targetDiv')innerHTML = "I did not find Nancy"; } } </script> </head> <body> <h1>Using the while loop</h1> <input type="button" onclick="display()" value="Click Here"> <div id="targetDiv"> </div> </body> </html>

method of finding phase angle in a circuit containing resistance and capacitive reactance This method shows the actual impedance vector

A shortcut was used to set up two variables here, loopIndex and the students array, which were declared like this, all in a single line: var loopIndex = 0, students = new Array(6);