Question

16．自耦理想變壓器示意圖如右．a(chǎn)b端為輸入端，接有效值始終為U₁的正弦交變電流；cd為輸出端，接有阻值為R的定值電阻．用以下哪些方法可以使輸入電流I₁增大（　　）
①只將P向下移；                         
②只將Q向下移；
③將P、Q向上移動(dòng)同樣的距離； 
④將P、Q向下移動(dòng)同樣的距離．

• A． ①④
• B． ②③
• C． ①③
• D． ②④

Answer 1

分析 根據(jù)電壓與匝數(shù)成正比，電流與匝數(shù)成反比，變壓器的輸入功率和輸出功率相等，逐項(xiàng)分析即可得出結(jié)論．

解答 解：根據(jù)電壓與匝數(shù)成正比，$\frac{{U}_{1}^{\;}}{{U}_{2}^{\;}}=\frac{{n}_{1}^{\;}}{{n}_{2}^{\;}}$，得${U}_{2}^{\;}=\frac{{n}_{2}^{\;}}{{n}_{1}^{\;}}{U}_{1}^{\;}$
根據(jù)輸入功率等于輸出功率，${U}_{1}^{\;}{I}_{1}^{\;}={U}_{2}^{\;}{I}_{2}^{\;}$=$\frac{{U}_{2}^{2}}{R}$=$\frac{（\frac{{n}_{2}^{\;}}{{n}_{1}^{\;}}{U}_{1}^{\;}）_{\;}^{2}}{R}$
解得：${I}_{1}^{\;}=\frac{{n}_{2}^{2}{U}_{1}^{\;}}{{n}_{1}^{2}R}$，只要$\frac{{n}_{2}^{\;}}{{n}_{1}^{\;}}$增大，${I}_{1}^{\;}$就增大
①只將P向下移，${n}_{1}^{\;}$減小，$\frac{{n}_{2}^{\;}}{{n}_{1}^{\;}}$增大，${I}_{1}^{\;}$就增大
②只將Q向下移，${n}_{2}^{\;}$減小，$\frac{{n}_{2}^{\;}}{{n}_{1}^{\;}}$減小，${I}_{1}^{\;}$就減小
③將P、Q向上移動(dòng)同樣的距離，$\frac{{n}_{2}^{\;}}{{n}_{1}^{\;}}$減小，${I}_{1}^{\;}$減小
④將P、Q向下移動(dòng)同樣的距離，$\frac{{n}_{2}^{\;}}{{n}_{1}^{\;}}$增大，${I}_{1}^{\;}$增大
故選：A

點(diǎn)評(píng) 掌握住理想變壓器的電壓、電流及功率之間的關(guān)系，本題即可得到解決．