Schwarz不等式在交流电有效值中的应用

Application on Schwarz Inequality in Effective Value of Alternating Current

交流电有效值是描述交流电的重要物理量,是高考的Ⅰ类考察内容.在考察学生对有效值理解的题目中,存在一些命题误区需要注意.例如电功率P=UI、并联电路电流I=I1+I2、串联电路电压U=U1+U2等直流电中常用公式,在交流电中不能随意套用.通过应用Schwarz不等式,从原理上说明这些公式的使用条件,在命题的时候需要引起重视.

The effective value of alternating current,an important physical quantity used to describe alternating current,is key content of the National College Entrance Examination.When setting questions to examine students′understanding of the effective value,we need to avoid some errors.The formulas commonly used in direct current cannot arbitrarily applied to alternating current,such as,[WTBX]P=UI,I=I 1+I 2,U=U 1+U 2,and so on.In this paper,the Schwarz inequality is applied to explain the conditions of the use of these formulas in principle.We need to pay attention to them when preparing test questions.