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    2019-2020學年高中物理全冊模塊要點回眸第12點把握“等效”緊扣“三同”求交變電流的有效值學案粵教版選修3-2
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    第12點 把握“等效”緊扣“三同”求交變電流的有效值
    有效值是交變電流中最重要的物理量,必須會求解,特別是正弦式交變電流的有效值,應記住公式.
    1.求交變電流有效值的方法
    (1)利用IUE計算,只適用于正()弦式交變電流.
    (2)非正弦式交變電流有效值的求解應根據電流的熱效應進行計算,其中,交變電流的有效值是根據電流通過電阻時產生的熱效應定義的,即讓交變電流和恒定電流通過相同的電阻,在交變電流的一個周期內若產生的熱量相同,則交變電流(電壓)的有效值就等于這個恒定電流(電壓)的值,即求解交變電流有效值問題必須在相同電阻、相同時間、相同熱量的“三同”原則下求解.
    2.應用有效值要注意以下幾點
    (1)各種使用交變電流的用電器上所標的額定電壓、額定電流均指有效值.
    (2)交流電壓表和交流電流表所測的數值為交流電壓和電流的有效值.
    (3)在進行電功、電熱、電功率的計算時,所代入的交流電壓和電流的數值為有效值.
    (4)凡沒有特別說明的,指的都是有效值.通常所說的家庭電路電壓是220V就是指的電壓的有效值.
    對點例題 如圖1所示是一交變電壓在一個周期內隨時間變化的圖象,求此交變電壓的有效值.
    1
    解題指導 設非正弦交變電壓的有效值為U,恒定電壓為U,讓非正弦交變電壓和恒定電壓分別加在同一電阻(設阻值為R)的兩端,在一個周期(T0.4s)內,非正弦交變電壓產生的熱量:
    Qt1t2t3t4
    ×0.1×0.1×0.1×0.1
    在這一個周期內,恒定電壓產生的熱量
    QT
    QQ,得
    所以UVUUV.
    答案 V
    1.如圖2表示一交變電流隨時間變化的圖象.其中,從t0開始的每個時間內的圖象均為半個周期的正弦曲線.求此交變電流的有效值.
    2
    答案 A
    解析 此題所給交變電流雖然相鄰半個周期的最大值不同,但在任意一個周期內,前半周期和后半周期的有效值是可以求的,分別為I1AI2A
    設所求交變電流的有效值為I,根據有效值的定義,選擇一個周期的時間,利用在相同時間內通過相同的電阻所產生的熱量相等,由焦耳定律得I2RTI12RI22R,即I22×2×,解得IA.
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