电路中求支路的电流的简便方法

Ⅰ 搴旂敤鏀璺鐢垫祦娉曡＄畻钖勬敮璺鐢垫祦镄勫叿浣撴ラゆ湁鍝浜

搴旂敤鏀璺鐢垫祦娉曡＄畻钖勬敮璺鐢垫祦镄勫叿浣撴ラゆ湁鍝浜涳纻鐩稿叧鍐呭瑰备笅锛

1锛夐栧厛鍦ㄧ数璺锲句腑镙囧嚭钖勬敮璺镄勭数娴佺殑鍙傝冩柟钖戙

瀵逛簬绾挎х数璺锛屽簲鐢ㄦ敮璺鐢垫祦娉曟椂锛岀数璺鍐呬笉鑳藉惈链夊帇鎺у厓浠舵瀯鎴愮殑鏀璺銆傚洜涓鸿繖绉嶆敮璺镄勭数铡嬫棤娉曢氲繃鐢垫祦𨱒ヨ〃杈撅纴浠庤屼篃灏辨棤娉曚粠KVL鏂圭▼涓娑埚幓璇ユ敮璺镄勭数铡嬨傚彟澶栵纴褰挞亣鍒扮数璺锛堜笉绠℃槸绾挎ц缮鏄闱炵嚎镐э级钖浠呯敱镫绔嬬数娴佹簮鏋勬垚镄勬敮璺镞讹纴链濂戒娇鐢ㄧ数婧愯浆绉绘硶灏呜ョ数娴佹簮杩涜岃浆绉伙纸瑙佺数璺鍙樻崲锛変互钖庯纴鍐岖敤鏀璺鐢垫祦娉曡繘琛岃＄畻銆

鏀璺鐢垫祦娉曚互鏀璺鐢垫祦浣滀负姹傝В瀵硅薄锛屽簲鐢ㄥ熀灏旈湇澶瀹氩緥鍒嗗埆瀵硅妭镣瑰强锲炶矾鍒楀啓镓闇镄勬柟绋嬬粍锛岀劧钖庤В鏂圭▼缁勬眰寰楀悇鏀璺鐢垫祦锛屼笖鍙浠ヨ繍鐢ㄦу嗗畾寰嫔缑鍒板悇𨱒℃敮璺涓婄殑鐢靛帇鍊笺

Ⅱ 濡备綍姹傝В鏀璺鐢垫祦锛

1锛塼=0 鍓嶏纴鐢佃矾涓鐢垫祦涓0锛屽嵆 iL(0) = 0锛孶c(0) = U锛

2锛塼>0 钖庯纴姝ょ数璺瀹为檯涓婂彲鍒嗕负涓ら儴鍒嗭纴濡备笅锲剧ず锛

镓姹傜殑鏀璺鐢垫祦锛屽氨鏄杩欎袱閮ㄥ垎鐢佃矾鐢垫祦镄勫彔锷狅绂

鏄剧劧瀵逛簬鐢垫劅鐢佃矾锛宨L(鈭) = U/R1锛屉1 = L/R1锛

钥屽逛簬鐢靛圭数璺锛孶c(鈭) = 0锛浵2 = C*R2 锛

2锛夊垎鍒浠ｅ叆鍏ㄥ搷搴斿叕寮忥纴寰 iL(t)銆乁c(t) 琛ㄨ揪寮忥绂

闾ｄ箞 i =iL(t) + Uc(t)/R2锛

濂戒简镊宸卞幓瀹屾垚钖э纴涓嶆哕鍙杩介梾锛

Ⅲ 骞惰仈鐢佃矾涓锛屽悇鏀璺鐢垫祦镐庢牱璁＄畻

骞惰仈鐢佃矾涓骞茶矾涓镄勭数娴佷笌鏀璺涓镄勭数娴佺殑鍏崇郴鏄骞惰仈鐢佃矾涓骞茶矾鐢垫祦绛変簬钖勬敮璺鐢垫祦涔嫔拰銆骞茶矾鐢垫祦琛ㄧ殑绀烘暟绛変簬鏀璺鐢垫祦琛ㄧ殑绀烘暟涔嫔拰锛屽苟镵旂数璺涓骞茶矾鐢垫祦绛変簬钖勬敮璺鐢垫祦涔嫔拰锛屽苟镵旂数璺涓骞茶矾鐢垫祦绛変簬钖勬敮璺鐢垫祦涔嫔拰銆

L1鍜孡1骞惰仈锛岀数娴佽〃A浣崭簬骞茶矾锛岀数娴佽〃A1浣崭簬L1鏀璺锛岀数娴佽〃A2浣崭簬L2鏀璺锛岀数璺锲惧拰杩炴帴瀹炵墿銆

骞惰仈鐢佃矾鐗圭偣

瀹氢箟骞惰仈鐢佃矾鏄浣垮湪鏋勬垚骞惰仈镄勭数璺鍏冧欢闂寸数娴佹湁涓𨱒′互涓婄殑鐩镐簰镫绔嬮氲矾锛屼负鐢佃矾缁勬垚浜岀嶅熀链镄勬柟寮忎箣涓銆备緥濡傦纴涓涓鍖呭惈涓や釜鐢电伅娉″拰涓涓9 V鐢垫睁镄勭亩鍗旷数璺銆傝嫢涓や釜鐢电伅娉″垎鍒鐢变袱缁勫肩嚎鍒嗗紑鍦拌繛鎺ュ埌鐢垫睁锛屽垯涓ょ伅娉′负骞惰仈銆

鐢佃矾链夊氭浔璺寰勶纴姣忎竴𨱒＄数璺涔嬮棿浜掔浉镫绔嬶纴链変竴涓鐢佃矾鍏冧欢寮璺锛屽叾浠栨敮璺镦у父宸ヤ綔锛屽崟浣嶅湪杩欓噷鍙娴嬮噺镄勫彉閲忔槸R鐢甸樆鍗曚綅娆у嗭纸惟锛夛纴I鐢垫祦鍗曚綅瀹夊煿锛圆锛夛纸搴扑粦姣忕掞级鍜孶鐢靛帇鍗曚綅浼忕壒锛圴锛夛纸铹﹁虫疮搴扑粦锛夈

骞惰仈鐢佃矾涓鐢ㄥ肩嚎杩炴帴鍦ㄧ数婧愪袱鏋佺殑浠绘剰涓ょ偣闂寸殑鐢靛帇鐩哥瓑銆傜数璺涓姣忎釜鐜璺涓镄勭数娴佺敱娆у嗗畾寰嫔缑鍑虹数铡嫔苟镵旂数璺涓钖勭数阒荤殑鐢靛帇涓庢荤数铡嬬浉钖岋纴閲岖偣镐庢牱鐪嫔浘镀忚В鍐冲苟镵斿拰涓茶仈

瀹氢箟娉曡瘑鍒涓茶仈鐢佃矾涓洪栧熬鐩歌繛锛屽苟镵旂数璺涓洪栭栫浉杩烇纴灏惧熬鐩歌繛锛岀数娴佹硶鐪嬬数璺涓鐢垫祦链夋病链夊垎鏀锛岀数娴佸嬬粓涓𨱒￠亾娌℃湁鍒嗘敮涓轰覆镵旓纴链夊垎链夊悎鍒欎负骞惰仈銆

𨰾嗛櫎娉曪纸链绠＄敤镄勪竴绉嶏级𨰾嗗嚭锛堟媶鎺夛级涓涓鐢ㄧ数鍣ㄤ娇杩欎竴鐢垫柇寮锛岀湅链夋病链夊奖鍝嶅埌鍏朵粬镄勭敤鐢靛櫒姝ｅ父宸ヤ綔锛屽奖鍝嶅埌浜嗗垯涓轰覆镵旓纴娌℃湁褰卞搷鍒板垯涓哄苟镵斻

Ⅳ 璇旷敤鏀璺鐢垫祦娉曟眰鐢佃矾涓钖勬敮璺镄勭数娴

鐢ㄦ敮璺鐢垫祦娉曪纴涓岖℃槸鍦╝镣硅缮鏄鍦╞镣癸纴涔熷彧鑳藉缑鍒颁竴涓鏂圭▼銆傚嵆锛
鈪=鈪1+鈪2锛屽浘涓宸茬煡鈪2=锛1A锛屾墍浠ュ纺瀛愪负锛
鈪=鈪1-1钬︹︹︹︹憼

蹇呴’寰楀熷姪鍙虫嗕袱锲炶矾鍦╝銆乥涓ょ偣涔嬮棿镄勭数铡嬶纴镓嶈兘寰楀埌绗浜屼釜鏂圭▼锛
鈪*35惟=20V-鈪1*10惟锛屽嵆锛
15*鈪=20+10鈪1钬︹︹︹︹憽

镵旇В鈶犮佲憽锛堜簩鍏冧竴娆℃柟绋嬬粍锛夛纴鍗冲彲寰楀埌鈪犮佲厾1镄勭瓟妗

灏嗏憼甯﹀叆鈶″缑鍒帮细
15*锛堚厾1-1锛=20+10鈪1
鏁寸悊钖庡缑鍒帮细
5鈪1=35
寰
鈪1=7A
灏嗏厾1镄勫煎甫鍏モ憼锛屽缑锛
鈪=7-1=6A

Ⅳ 濡备綍姹傛敮璺鐢垫祦镄勮〃杈惧纺锛

鍏锋湁l=b-n+1涓锘烘湰锲炶矾镄勭嚎镐х数璺镄勫洖璺鏂圭▼镄勪竴鑸褰㈠纺鏄锛
锛1锛
寮忎腑Rij锛坕=1,2,钬︼纴l锛夋槸锲炶矾i涓镄勬墍链夌数阒讳箣鍜岋纴绉颁负锲炶矾i镄勮嚜鐢甸樆锛汻ij锛坕銆乯=1钬l,i铌爅锛夋槸锲炶矾i涓庡洖璺痡 镓鍏辨湁镄勭数阒伙纸浜掔数阒伙级锛屽湪锲炶矾鐢垫祦Ii涓庣数娴両j鍦ㄥ叡链夋敮璺涓鏂瑰悜鐩稿弽镞讹纴杩桦簲涔树互-1锛沄si鏄锲炶矾i涓钖勭数锷ㄥ娍镄勪唬鏁板拰銆
鎺屾彙浜嗛氱敤锲炶矾鏂圭▼镄勫舰寮忓拰鍐呭癸纴鍙浠ュ緢蹇鍦扮洿鎺ュ嚟瑙傚疗鍐椤嚭涓涓鐢佃矾镄勫洖璺鏂圭▼銆
锲炶矾鐢垫祦娉
褰撶数璺鍐呮湁濡傚浘a镓绀虹殑鏀璺镞讹纴鍙灏嗗叾鍙樻崲鎴愬傚浘b镓绀虹殑鏀璺锛岀劧钖庡啀鍒楀啓鏂圭▼銆傚纺锛1锛夊彲绠璁颁负
锛2锛
寮忎腑鍨炬槸浠ヨ嚜鐢甸樆銆佷簰鐢甸樆涓哄厓绱犵殑l脳l鐭╅樀锛坙=b-n+1锛夛纴Il鏄浠ュ洖璺鐢垫祦涓哄垎閲忕殑l缁寸煝閲忥纴VS鏄寮忥纸1锛夌殑鍙崇椤逛负鍒嗛噺镄刲缁寸煝閲忋
瀵圭数璺杩涜屾ｅ鸡绋虫佸垎鏋愭椂锛岀敤鐩搁噺娉曞拰锲炶矾鐢垫祦娉曞啓鍑虹殑锲炶矾鏂圭▼涓
锛3锛
瀵圭数璺杩涜屾殏镐佸垎鏋愭椂锛岀敤𨰾夋櫘𨰾夋柉鍙樻崲鍜屾ゆ硶鍐椤嚭镄勫洖璺鏂圭▼涓
锛4锛