题干

两个定值电阻R1和R2,若R1=R0, R2=nR0  两个电阻可以任意组合分别接在某电压不变的同一电路中,请证明电路最大总功率和电路最小总功率比值为:(n+1)2/n

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答案(点此获取答案解析)

解:根据P=
U
2
R
,可知电路中电压一定,总电阻最小时,总功率最大,总电阻最大时,总功率最小。两电阻并联时总电阻最小,所以总功率最大,串联时,总电阻最大,所以总功率最小。
两电阻并联在电压为U的电路中

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    About 70 scientists were working on a very busy project. All of them felt really desperate due to the pressure of work and the demands of their boss but everyone was loyal to him and did not think of quitting their job.

    One day, one scientist came to his boss and told him, “Sir, I've promised to take my children to the exhibition going on in our township so I want to leave at 5:30 p. m.” His boss replied, “OK. You're permitted to leave the office early today.”

    The scientist started working. He continued his work after lunch. As usual, he got involved to such an extent that he looked at his watch only when he felt he was close to completion. The time was 8:30 p. m. suddenly he remembered his promise to the children. He looked for his boss but he was not there. Having told him in the morning himself, he closed everything and left for home. Deep within himself, he was feeling guilty for having disappointed his children. He reached home. The children were not there. His wife alone was sitting in the hall and reading magazines. The situation was explosive; any talk would boomerang on him. His wife asked him, “Would you like to have coffee or shall I straight away serve dinner if you are hungry?” The man replied, “If you would like to have coffee, I too will have but what about the children?” His wife replied, “You don't know? Your boss came here at 5:15 p. m. and has taken them to the exhibition.”

    What had really happened was the boss who gave him permission was observing him working seriously at 5:00 p. m. He thought to himself: this person will not leave the work, but he's promised to take his children to the exhibition. So he took the lead in taking them there. The boss does not have to do it every time. But once it's done, loyalty is established.

    That is why all the scientists at Thumba continued to work under their boss even though the stress was extraordinarily huge. By the way, can you boldly guess who the boss was? He was none other than the mastermind behind India's successful nuclear weapons program, Dr. APJ Abdul Kalam, former president of India.