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如图所示，某村在距村庄较远的地方建了一座小型水电站，发电机的输出功率为9kW，输出电压为500V，

输电线电阻为10Ω，允许线路消耗的功率为输出功率的4%，求：

（1）若不用变压器而由发电机直接输送，用户得到的电压和功率是多少？

（2）用如图所示电路输电，若用户需要220V电压时，所用升压、降压变压器原副线圈匝数比为多少？（不计变压器能量损失）

答案

（1）不用变压器而直接输送时，

输电线上的电流I=

P
U
=
9×103
500
A=18A

电压损失△U=IR=18×10V=180V

功率损失△P=I2R=182×10=3240W

用户得到的电压和功率分别是

U用=U-△U=500V-180V=320V

P用=P-△P=9000W-3240W=5760W

（2）由△P=P×4%=I2R

代入数据得I2=6A，

由P=U2I2得

U2=

P
I2
=
9000
6
V=1.5×103V

由=

n1
n2
=
u1
u2

得

n1
n2
=
500
1500
=
1
3

U3=U2-I2R=（1500-60）V=1440V

所以

n3
n4
=
u3
u4
=
1440
220
=
72
11

答：（1）若不用变压器而由发电机直接输送，用户得到的电压为320V，功率是5760W．

（2）用如图所示电路输电，若用户需要220V电压时，所用升压、降压变压器原副线圈匝数比分别为

1
3
和
72
11
．

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