å·²ç»åçè¿äºï¼ä¸ç¥éæ¯ä¸æ¯ä½ çæé®ãç½é¡µé¾æ¥
解ï¼ä½¿ç¨å å å®çãéæ£å¼¦å¨æçµè·¯åæçç¸å ³ç¥è¯ã
çµè·¯å®é æä¸ä¸ªæ¿å±æºï¼äº¤æµçµåæºã交æµçµæµæºåç´æµçµæµæºï¼åå«è¿è¡è®¡ç®ã
1ãçµåæºåç¬ä½ç¨æ¶ï¼çµæµæºå¼è·¯ãæ¤æ¶10Ωçµé»æ çµæµãæ çµåï¼å æ¤u'å°±çäºçµæ两端çµåãUsï¼ç¸éï¼=3/â2â 0°=2.1213â 0°Vï¼Ï=3rad/sãXL=3Ã0.5=1.5Ωï¼Xc=1/ï¼ÏCï¼=1/ï¼3Ã0.1ï¼=10/3ï¼Î©ï¼ã
U'ï¼ç¸éï¼=Usï¼ç¸éï¼Ãj1.5/jï¼1.5-10/3ï¼=2.1213â 0°Ãï¼-9/11ï¼=-1.7356=1.7356â 180°ï¼Vï¼ã
2ã交æµçµæµæºåç¬æ¿å±æ¶ï¼ç´æµçµæµæºæå¼ãçµåæºçè·¯ã
æ¤æ¶ï¼i1s=cos3t=cosï¼-3tï¼=sin[90°-ï¼-3tï¼]=sinï¼3t+90°ï¼ï¼å³ï¼I1sï¼ç¸éï¼=1/â2â 90°=0.707â 90°ï¼Aï¼ã
æ»é»æï¼Z=10+j1.5â¥ï¼-j10/3ï¼=10+j2.7273=10.3652â 15.26°ï¼Î©ï¼ã
æ以ï¼U"ï¼ç¸éï¼=I1sï¼ç¸éï¼ÃZ=0.707â 90°Ã10.3652â 15.26°=7.3282â 105.26°=-1.9288+j7.0698ï¼Vï¼ã
3ãç´æµçµæµæºåç¬ä½ç¨æ¶ï¼äº¤æµçµæµæºå¼è·¯ãçµåæºçè·¯ãåæ¶çµæçè·¯ãçµå®¹å¼è·¯ã
U'"=I2sÃR=2Ã10=20ï¼Vï¼ã
4ãå å ï¼ç±äº1ãå2ãä¸é½æ¯åé¢ççæ¿å±ä¿¡å·ï¼æ以ç¸åºå¯ä»¥è¿è¡ç¸éç¸å ï¼U12(ï¼ç¸éï¼=U'ï¼ç¸éï¼+U"ï¼ç¸éï¼=-1.7356-1.9288+j7.0698=-3.6644+j7.0698=7.963â 117.4°ï¼Vï¼ã对åºäºç¬æ¶å¼è¡¨è¾¾å¼ï¼u12ï¼tï¼=7.963â2sinï¼3t+117.4Â°ï¼ Vã
æ以ï¼uï¼tï¼=20+7.963â2sinï¼3t+117.4Â°ï¼ ï¼Vï¼ã
çµæµæºä¸å å«ç´æµåéï¼I2s=2Aï¼ååºU'"=20Vï¼æ以ï¼P1=2Ã20=40W>0ï¼ä¸çµåãçµæµä¸ºéå ³èæ£æ¹åï¼ç´æµåéæä¾åç40Wï¼
çµæµæºä¸ç交æµåéï¼I1s=1/â2=0.707Aï¼ææå¼ï¼ï¼Ïi=90°ï¼U"=7.3282Vï¼ææå¼ï¼ï¼Ïu=105.26°ãæ以Ï=Ïu-Ïi=105.26°-90°=15.26°ãP2=U'"ÃI1sÃcosÏ=7.3282Ã0.707Ãcos15.26°=5ï¼Wï¼ãåæ ·ç±äºéå ³èæ£æ¹åï¼æ以交æµçµæµæºæä¾åç5Wãââï¼å®é ä¸ï¼çµè·¯ä¸å°å¹³ååççåªæ¯çµé»ï¼èçµæµæºä¸çµé»ä¸²èï¼æ以çµæµæºäº¤æµåéæä¾åçå¯ä»¥ç®åçï¼P2=I1s²R=ï¼1/â2ï¼²Ã10=5Wãï¼
å æ¤çµæµæºæä¾çå¹³ååç为ï¼P=P1+P2=40+5=45ï¼Wï¼ã