如图所示,两条平行的光滑金属导轨固定在倾角为θ的绝缘斜面上,导轨上端连接一个定值电阻.导体棒a和b放在导轨上,与导轨垂直开良好接触.斜面上水平虚线PQ以下区域内,存在着垂直穿过斜面向上的匀强磁场.现对a棒施以平行导轨斜向上的拉力,使它沿导轨匀速向上运动,此时放在导轨下端的b棒恰好静止.当a棒运动到磁场的上边界PQ处时,撤去拉力,a棒将继续沿导轨向上运动一小段距离后再向下滑动,此时b棒已滑离导轨.当a棒再次滑回到磁场上边界PQ处时,又恰能沿导轨匀速向下运动.已知a棒、b棒和定值电阻的阻值均为R,b棒的质量为m,重力加速度为g,导轨电阻不计.求                                                                                                                                      

(1)a棒在磁场中沿导轨向上运动的过程中,a棒中的电流强度Ia与定值电阻中的电流强度Ic之比;                                                                                                                                                      

(2)a棒质量ma;                                                                                                        

(3)a棒在磁场中沿导轨向上运动时所受的拉力F.                                                           

                                                                   

                                                                                                                                      


质量为m边长为l的正方形线框,从有界的匀强磁场上方由静止自由下落,线框电阻为R,匀强磁场的宽度为H(H>l),磁感强度为B,线框下落过程中ab边与磁场界面平行.已知ab边刚进入磁场和刚穿出磁场时都作减速运动,加速度大小均为a=g/3.试求:                                                                                                                

(1)ab边刚进入磁场时,线框的速度;                                                                             

(2)cd边刚进入磁场时,线框的速度;                                                                             

(3)线框经过磁场的过程中产生的热能.                                                                          

                                                                                               

                                                                                                                                      


为了节能和环保,一些公共场所使用光控开关控制照明系统.光控开关可采用光敏电阻来控制,光敏电阻是阻值随着光的照度而发生变化的元件(照度可以反映光的强弱,光越强照度越大,照度单位为Lx).某光敏电阻Rp在不同照度下的阻值如下表:                                                                                                                        

照度(Lx)  0.2   0.4   0.6   0.8   1.0  1.2

电阻(k)    75    40    28    23    20   18

①根据表中数据,请在给定的坐标系中描绘出阻值随照度变化的曲线(图1),并说明阻值随照度变化的特点.                                                                                                                                              

②如图2所示,当1、2两端所加电压上升至2V时,控制开关自动启动照明系统,                                         

                                                  

请利用下列器材设计一个简单电路.给1、2两端提供电压,要求当天色渐暗照度降低至1.0(Lx)时启动照明系统,在虚线框内完成电路原理图.(不考虑控制开关对所设计电路的影响)提供的器材如下:光敏电阻Rp,电源E(电动势3V,内阻不计),定值电阻:R1=10k,R2=20k,R3=40k(限选定值电阻其中之一并在图中标出),开关S及导线若干.                                                                                                                                              

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