问题 计算题

(14分)如图所示,固定在水平桌面上的光滑金属导轨MN、PQ,间距为L,其右端接有阻值为R的电阻和理想交流电压表,整个装置处在竖直向下的匀强磁场中,磁感应强度大小为B.导体棒ef垂直于导轨放置,且与两导轨接触良好,导体棒接入电路的电阻为r,其它电阻不计,现让导体棒在ab、cd之间往复运动,其速度随时间的关系为(vm和T已知).

(1)写出导体棒产生的电动势的表达式,并求出电压表的示数;

(2)求一个周期T内R中产生的焦耳热Q;

(3)若ab与cd的距离为x,求导体棒从ab滑到cd过程中通过电阻R的电量q.

答案

⑴e=,UR;⑵Q=;⑶q=

题目分析:⑴根据法拉第电磁感应定律可知导体棒由于切割磁感线而产生的感应电动势为:e=BLv ①

又因为v=         ②

根据闭合电路欧姆定律可知,电阻R两端的电压瞬时值为:u=      ③

由①②③式联立解得:e=,u=

显然R两端的电压瞬时值随时间t成正弦函数关系变化,又根据电路分析可知,电压表测出的是电阻R两端电压的有效值,因此其读数为:UR          ④

根据焦耳定律可知,在一个周期T内R中产生的焦耳热为:Q=          ⑤

由④⑤式联立解得:

⑶根据电流的定义式可知,在导体棒从ab滑到cd过程中通过电阻R的电量为:q=     ⑥

根据闭合电路欧姆定律有:     ⑦

根据法拉第电磁感应定律可知:      ⑧

在导体棒从ab滑到cd过程中,回路中的磁通变化量为:ΔΦ=BΔS=BLx    ⑨

由⑥⑦⑧⑨式联立解得:q=

阅读理解

They say love can cover a lot of crimes; yet never have I seen it more beautifully showed than in the life of a dog named Jessie. Jessie came into our lives at the age of six months. By that time he had already experienced the hard knocks of life. He was found abandoned on the side of the road, where we adopted him and took him home.

From the beginning, it was obvious that Jessie was traumatized (受精神创伤的). He was afraid of everything: the car, the doors, the stairs, and just about everything else. We couldn’t foresee where Jessie’s fear would take us.

Jessie was with us for about six months, when we became foster parents to a mixed-breed young dog. Jessie did not like her at all. We all lived in a nervous co-existence, until dinnertime. Within moments a food fight erupted between Jessie and this foster child.

It all happened so fast, and I was in the middle. My husband managed to get in between the two dogs, grabbing Jessie by his collar. Jessie screamed all the way down the hall and into the bedroom. I, quickly put the foster dog into her own bedroom and hurried down the hall. The crashing I heard in the bedroom, scared me to death. But nothing prepared me for the scene I witnessed as I opened the bedroom door.

There was my husband, on top of a terrified Jessie, holding back his head. Blood dripped from my husband’s arm. To tell you the truth, as I was sitting beside my husband in the emergency room, I just didn’t know what to do with Jessie. I was so angry at that dog.

Day after day, week after week, however, my husband faithfully trained the dog that others would have put down. As his arm healed over the next months, something rare and beautiful began to take place. Jessie, under my husband’s gentle persuasion, began to understand and obey. And Jessie adored him. I could see, that although the tempest had ruled Jessie’s former life, affirmation and love had calmed the storm.

小题1:Before being adopted by the writer, Jessie had _______.

A.suffered a lot

B.Lived a happy life

C.lived on the road half a year

D.often fought against other dogs小题2: Paragraph 2 shows that the writer was ________.

A.happy

B.disappointed

C.angry

D.worried小题3:It can be inferred from the text that the writer’s husband’s arm bled because   of _________.

A.his own behavior

B.the writer’s fault

C.Jessie’s bite

D.The new foster dog小题4:What would be the best title for the text?

A.A Dog Named Jessie

B.Love Calmed the Storm

C.Conflicts Between Dogs

D.Fights Between Man and Dog

单项选择题