Question

3．如图所示，一理想变压器由一个初级线圈和两个次级线圈组成，当此变压器工作时，初级和次级线圈的匝数、电流、电压均在图中标出，则下列几组关系式中正确的是（　　）

• A． $\frac{{U}_{1}}{{U}_{2}}$=$\frac{{n}_{1}}{{n}_{2}}$，$\frac{{U}_{1}}{{U}_{3}}$=$\frac{{n}_{1}}{{n}_{3}}$
• B． $\frac{{I}_{1}}{{I}_{2}}$=$\frac{{n}_{1}}{{n}_{2}}$，$\frac{{I}_{1}}{{I}_{3}}$=$\frac{{n}_{3}}{{n}_{1}}$
• C． n₁I₁+n₃I₃=n₂I₂
• D． $\frac{{I}_{1}}{{I}_{2}+{I}_{3}}$=$\frac{{n}_{2}+{n}_{3}}{{n}_{1}}$

Answer 1

分析 根据电压与匝数成正比，变压器的输入功率和输出功率相等，逐项分析即可得出结论．

解答 解：A、根据电压与匝数成正比，有$\frac{{U}_{1}^{\;}}{{U}_{2}^{\;}}=\frac{{n}_{1}^{\;}}{{n}_{2}^{\;}}$、$\frac{{U}_{1}^{\;}}{{U}_{3}^{\;}}=\frac{{n}_{1}^{\;}}{{n}_{3}^{\;}}$，故A正确；
B、由于副线圈是两个，电流与匝数不再成反比，故B错误；
C、根据理想变压器输入功率等于输出功率，所以有${U}_{1}^{\;}{I}_{1}^{\;}={U}_{2}^{\;}{I}_{2}^{\;}+{U}_{3}^{\;}{I}_{3}^{\;}$，电压与匝数成正比$\frac{{U}_{1}^{\;}}{{n}_{1}^{\;}}=\frac{{U}_{2}^{\;}}{{n}_{2}^{\;}}=\frac{{U}_{3}^{\;}}{{n}_{3}^{\;}}=k$
联立得$k{n}_{1}^{\;}{I}_{1}^{\;}=k{n}_{2}^{\;}{I}_{2}^{\;}+k{n}_{3}^{\;}{I}_{3}^{\;}$
得${n}_{1}^{\;}{I}_{1}^{\;}={n}_{2}^{\;}{I}_{3}^{\;}+{n}_{3}^{\;}{I}_{3}^{\;}$，故C错误；
D、$\frac{{I}_{1}^{\;}}{{I}_{2}^{\;}+{I}_{3}^{\;}}=\frac{{n}_{2}^{\;}+{n}_{3}^{\;}}{{n}_{1}^{\;}}$变形得${I}_{1}^{\;}{n}_{1}^{\;}=（{n}_{2}^{\;}+{n}_{3}^{\;}）（{I}_{2}^{\;}+{I}_{3}^{\;}）$=${n}_{2}^{\;}{I}_{2}^{\;}+{n}_{2}^{\;}{I}_{3}^{\;}+{n}_{3}^{\;}{I}_{2}^{\;}+{n}_{3}^{\;}{I}_{3}^{\;}$，由C分析知，D错误；
故选：A

点评 掌握住理想变压器的电压、电流及功率之间的关系，本题即可得到解决