实验报告：简易介电常数测试仪的设计与制作冷冬PB07204002数据处理：一．电流替代法组数Ix/mACs/uF11.270.029121.2630.028931.2610.028941.2590.028851.2620.028961.260.0288平均值1.26250.0289由公式：εr=4Cx*h/ε*πd^2=(4*0.0289*10^-6*0.194*10-3)/(3.14*8.85*10^-12*(24.65*10^-3)^2)=1.328*10^3不确定度分析：εr=4Cx*h/ε*πd^2两边对数求导得：即=(0.02*0.65%+0.008*2%+0.0009*5%)/0.0289=0.00457∴==4.78%∴εr=1.328*10^3±0.0047二．电压替代法组数Vx/vCs/uF13.5020.03223.710.028533.5080.031943.7060.028753.5110.031863.7020.0287平均值3.60650.030267由公式：εr=4Cx*h/ε*πd^2=(4*0.030267*10^-6*0.194*10-3)/(3.14*8.85*10^-12*(24.65*10^-3)^2)=1.342*10^3∴不确定度分析时只要改变的值即可。=(0.03*0.65%+0.002*2%+0.0007*5%)/0.0289=0.0093==5.24%∴εr=1.342*10^3±0.00524三．比较法组数Cs/uFVs/vVx/vCx/uF10.02674.5593.3890.03591820.0253.9433.2670.03017330.0234.0963.1150.03024340.0224.1733.0370.03022950.0263.8753.3390.03017460.0244.0143.20.030105由公式Cx=Cs*Vs/Vx求得了6组Cx的值求平均值得Cx=0.03114∵εr=4Cx*h/ε*πd^2=(4*0.03114*10^-6*0.194*10-3)/(3.14*8.85*10^-12*(24.65*10^-3)^2)=1.343*10^3∴不确定度分析时只要改变的值即可。=(0.03*0.65%+0.001*2%+0.0004*5%)/0.0289=0.008131==5.22%∴εr=1.343*10^3±0.00522四．谐振法组数f/HzCx/f1902.63.11236E-082913.653.03753E-083913.63.03787E-084922.052.98244E-085895.33.16332E-086909.843.06303E-08由公式Cx=求出6组Cx，再求平均值得：Cx=3.06609E-08f=0.0307ufεr=4Cx*h/ε*πd^2=(4*0.0307*10^-6*0.194*10-3)/(3.14*8.85*10^-12*(24.65*10^-3)^2)=1.410*10^3∴不确定度分析时只要改变的值即可。=(0.03*0.65%+0.0007*5%)/0.0289=0.007958==5.22%∴εr=1.410*10^3±0.00522五．谐振替代法组数f/HzCx/uf1907.860.3082894.050.3173917.560.3014903.30.315907.710.3076903.240.307∵Cx=Cs对Cx=0.3083εr=4Cx*h/ε*πd^2=(4*0.0308*10^-6*0.194*10-3)/(3.14*8.85*10^-12*(24.65*10^-3)^2)=1.410*10^3∴不确定度分析时只要改变的值即可。=(0.03*0.65%+0.0008*5%)/0.0289=0.007961==5.22%∴εr=1.410*10^3±0.00522思考题：该实验待测电容是由直径为3.502cm，厚度为0.092，上下表面镀有金属电极的压电陶瓷片构成，实验中没有考虑电容边缘效应的影响，若要克服电容边缘效应的影响应如何改进电极装置？答：要克服电容边缘效应的影响，需要在装置的边缘嵌套介电常数比较高的电介质，如塑料环等。
