题目内容

将定值电阻R1和R2串联后接在电压不变的电源上,R1消耗的功率为5W,R2消耗的功率为10W,若将它们并联后接在该电源上,它们消耗的总功率为______W.
当两电阻串联时,电路中各处的电流相等,
P1
P2
=
I2R1
I2R2
=
R1
R2
=
5W
10W
=
1
2
,即R2=2R1
电路消耗的总功率:
P=
U2
R1+R2
=
U2
R1+2R1
=
U2
3R1
=5W+10W=15W,
整理得:
U2
R1
=45W,
两电阻并联时,并联的总电阻:
R=
R1R2
R1+R2
=
R1×2R1
R1+2R1
=
2R1
3

电路消耗的总功率:
P=
U2
R
=
U2
2R1
3
=
3
2
×
U2
R1
=
3
2
×45W=67.5W.
故答案为:67.5.
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