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Trigonometric Method Using trigonometry, you can determine the RC phase angle more precisely than the pictorial method allows Given the values of X C and R, the RC phase angle is the arctangent of their ratio Phase angle in RC circuits is symbolized by the lowercase Greek letter , just as it is in RL circuits Here are the formulas:

Figure 2-14

= tan 1 (X C /R ) or = arctan (XC /R )

It can be very important for the Ajax programmer to know which browser the user has, because the browser is the way you communicate with the user, and different browsers have different capabilities (for example, Internet Explorer has a scrolling <marquee> element that Firefox doesn t have) You can use JavaScript in your Ajax-enabled web pages to determine which browser the user has To do that, you check the text string in the built-in navigator object s userAgent property (which you access in JavaScript as navigatoruserAgent) In JavaScript, text strings are actually objects with their own properties and methods, and to search a text string, you can use the string s indexOf method, which returns the index of a substring you re searching for in the main string (that is, the position the substring starts at in the main string, where the first character is character 0) If the substring is not found in the main string, indexOf will return a negative value So, for example, to see if the browser identification string held in navigatoruserAgent contains the text "Firefox" you could check the return value of the expression navigator userAgentindexOf("Firefox") if it s non-negative, the string navigatoruserAgent contains the word "Firefox" Besides the navigatoruserAgent string, there s also another string, navigatorappName, that this page, browserhtml, uses The navigtorappName string lets browserhtml make the first determination of the browser type if it holds "Netscape", you re dealing with Firefox (or Netscape Navigator), and if it holds "MSIE", you re dealing with Microsoft Internet Explorer Here s what browserhtml looks like (browserhtml):

<html> <head> <title> What browser do you do have </title> <script language="javascript"> var begin, end function display() { if(navigatorappName == "Netscape") { if(navigatoruserAgentindexOf("Firefox") > 0) { begin = navigatoruserAgentindexOf("Firefox") + "Firefox"length + 1; end = navigatoruserAgentlength; documentgetElementById("targetDiv")innerHTML = "You are using Firefox " + navigatoruserAgentsubstring(begin, end); } }

When doing problems of this kind, remember to use the capacitive reactance values for X C, and not the capacitance values This means that, if you are given the capacitance, you must use the formula for X C in terms of capacitance and frequency and then calculate the phase angle You should get angles that come out negative or zero This indicates that they re RC phase angles rather than RL phase angles (which are always positive or zero)

2:

Problem 14-4 Suppose the capacitive reactance in an RC circuit is 3800 and the resistance is 7400 What is the phase angle Find the ratio X C /R = 3800/7400 The calculator display should show you something like 0513513513 Find the arctangent, or tan 1, getting a phase angle of 2718111109 on the calculator display Round this off to 2718 Problem 14-5 Suppose an RC circuit works at a frequency of 350 MHz It has a resistance of 130 and a capacitance of 150 pF What is the phase angle First, find the capacitive reactance for a capacitor of 150 pF at 350 MHz Convert the capacitance to microfarads, getting C = 0000150 F Remember that microfarads go with megahertz (millionths go with millions to cancel each other out) Then:

if (navigatorappName == "Microsoft Internet Explorer") { begin = navigatoruserAgentindexOf("MSIE ") + "MSIE "length; if(navigatoruserAgentindexOf(";", begin) > 0) { end = navigatoruserAgentindexOf(";", begin); } else { end = navigatoruserAgentindexOf(")", begin) + 2; } documentgetElementById("targetDiv")innerHTML = "You are using Internet Explorer " + navigatoruserAgentsubstring(begin, end); } } </script> </head> <body> <h1>Determining browser type and version</h1> <input type="button" onclick="display()" value="Click Here"> <div ID="targetDiv"></div> </body> </html>