【公式】交变流电


1、正弦交变电流瞬时值和峰值(中性面开始)

(1)电动势:

    ①瞬时值:\(\begin{aligned}e&=E_{m}\sin \omega t\end{aligned}\)

    ②最大值:\(E_{m}=NBS \omega\sin \omega t\)

 

(2)输出电压:

    ①瞬时值:\(\begin{aligned}u=U_{m}\sin \omega t\end{aligned}\)

    ②最大值:\(U_{m}=E_{m}\cdot \dfrac {R}{R+r}\)

 

(3)电流 

    ①瞬时值:\(\begin{aligned}i=I_{m}\sin \omega t\end{aligned}\)

    ②最大值:\(I_{m}=\dfrac {U_{m}}{R+r}\)


2、正弦交变电流有效值

(1)电动势:\(E=\dfrac {E_{m}}{\sqrt {2}}\)

(2)电压:\(U=\dfrac {U_{m}}{\sqrt {2}}\)

(3)电流:\(I=\dfrac {I_{m}}{\sqrt {2}}\)


3、平均值

(1)电动势:\(\bar{E}=N\dfrac {\Delta \Phi }{\Delta t}\)

(2)电流:\(\bar{I}=\dfrac {\bar{E}}{R+r}\)


4、周期和频率

(1)周期:T是交变电流完成一次周期性变化所需的时间。

(2)频率:f是交变电流1s内完成周期变化的次数。

(3)关系:

    ①\(T=\dfrac {2\pi }{\omega }\)

    ②\(f=\dfrac {1}{T}=\dfrac {\omega }{2\pi }\)


5、电容和电感对交变电流的影响

(1)容抗公式:\(R_{C}=\dfrac {1}{2\pi fC}\)

(2)感抗公式:\(R_{L}={2\pi fL}\)


6、理想变压器

(1)电压关系

    ①一个副线圈:\(\dfrac {U_{1}}{n_{1}}=\dfrac {U_{2}}{n_{2}}\)

    ②多个副线圈:\(\dfrac {U_{1}}{n_{1}}=\dfrac {U_{2}}{n_{2}}=\dfrac {U_{3}}{n_{3}}=\ldots\)

 

(2)电流关系

    ①一个副线圈:\(\dfrac {I_{1}}{I_{2}}=\dfrac {n_{2}}{n_{1}}\)

    ②多个副线圈:\(I_{1}n_{1}=I_{2}n_{2}=I_{3}n_{3}=\ldots\)

 

(3)功率关系:输入功率等于输出功率

    ①总功率相等:\(P_{出}=P_{入}\)

    ②一个副线圈:\(I_{1}U_{1}=I_{2}U_{2}\)

    ③多个副线圈:\(I_{1}U_{1}=I_{2}U_{2}+I_{3}U_{3}+\ldots\)

 

(4)频率关系:\(f_{1}=f_{2}\)