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1、论文分类号：0441.1密 级：论文题目电容取值对RLC串/并联谐振电路实验误差的影响目录摘 要 1引 言 11 实验部分 31.1 实验设备31.2电容取值对RLC串联谐振电路实验误差的影响31.3电容取值对RLC并联谐振电路实验误差的影响42 结果与讨论 62.1电容取值对RLC串联谐振电路实验数据的分析62.2电容取值对RLC并联谐振电路实验数据的分析73 结 论 8参考文献 9电容取值对 RLC 串/并联谐振电路实验误差的影响摘 要：RLC串/并联谐振是交流电路中的一种特殊现象，在电工技术和 无线电中得到广泛的应用。本论文通过确定电阻和电感值，采用测量电 路中电阻或电容两端电压为最大值
2、的办法来确定谐振频率，讨论了电容 数值对测量误差的影响。实验结果表明，不论在串联谐振还是并联谐振 实验中，都是电容取值越小，谐振频率的测量值越准确。关键词：RLC串/并联电路；电容；谐振频率The effect of the capacitance on the RLC series/parallelresonanceZhang Jing(Class 5 Grade 2010 in College of Physics, Jilin Normal University, Jilin Siping 136000) Directive teacher: Wang Li (lecturer)Abst
3、ract: RLC series / parallel circuit is a particular phenomenon in ac circuit, and widely be used in fields of electrical technology and radio. In this paper, we study the effect of the capacitance on the RLC series/parallel resonance through measuring the maximum of voltage of the resistor or capaci
4、tor. The results show that the value of capacitance is smaller; the accuracy of RLC series / parallel circuit is the better.Key words: RLC series / parallel circuit; the capacitance; resonant frequency引言RLC 串/并联谐振是交流电路中的一种特殊现象，在电工技术和无线电中得到广 泛的应用。对于RLC串/并联谐振，普通物理实验通常要求在品质因数Q1的 情况下，采用测量电路中电阻或电容两端电压为最大
5、值的办法来确定谐振频率。串联 RLC 电路由电阻、电感和电容组成的。由于感抗和容抗对电路相位角的作 用相反，所以总的电抗小于任何一个单独的电抗。已知容性阻抗随频率增大而减小， 感抗随频率增大而增大。图1是RLC串联电路中总电抗的变化规律：电源频率逐渐 增大，当频率非常小时，容抗较高，感抗较低，电路呈电容性。随着频率的逐渐升高， 容抗随之减小，感抗逐渐增大，当容抗等于感抗的时候，两者的电抗效应互相抵消， 电路可以简化为纯电阻电路，即串联谐振的条件。随着频率的继续增大，感抗大于容当XC=XL时，RLC串联电路发生谐振，发生谐振的频率叫做串联谐振频率，串 联谐振又称作电压谐振。并联 RLC 电路也是
6、由电阻、电感和电容组成的。在并联电路中，感抗越小对电 路的影响就越大，因为电抗越小，支路电流就越大。当频率较低时，xcxl,电路呈感 性的。随着频率的增大，容抗减小，感抗增大，当xc=xl时，就是并联谐振，又称 为电流谐振，此时的频率为RLC并联谐振频率。当频率继续增大时，XCXL,电路呈 容性的。本文采用测量电路中电阻或电容两端电压为最大值的办法来确定RLC串/并联谐 振频率的实验值，电容取值对谐振频率测量的影响。1 实验部分1.1 实验设备表1实验所用设备名称型号出厂商信号发生器YB163P电阻箱ZX38A/10交/直流自感器BG 6/4型标准十进制电容箱RX7型交流毫伏表AS2173D1
7、.2 电容取值对 RLC 串联谐振电路实验误差的影响ab图 2 RLC 串联电路图电路图见图2,已知电感内阻Rl=20Q,电阻取值500、1000和1500。电容C取 值分别为 0.01yF、0.03yF、0.05yF、0.1yF、0.15yF、0.2yF、0.3yF、0.4yF 和 0.5yF。 测量时保持a、b两端电压为1.06V。用交流毫伏表测电阻两端电压，当电压为最大 时，电路达到谐振状态。记录此时的频率值，即谐振频率的测量值f测，连续测量五 次，求其平均值f平均，实验数据见表2。表 2 串联电路 R 与 C 取不同值时测量的谐振频率的测量值0.014.9954.9854.9905.0
8、214.4844.8950.023.5723.5483.5593.5683.5513.55920.032.8922.8842.9012.8982.9052.8960.052.2422.2532.2432.2332.2412.2418R=50Q0.11.5871.5911.6031.5921.5901.59260.151.3091.2901.3021.3041.2981.30060.21.1321.1171.1211.1261.1241.1240.30.9170.9140.9240.9200.9110.91720.40.7880.7900.8020.7950.7850.7920.50.7090.
9、7150.7130.7060.7070.710.015.0104.9995.0065.0095.0015.00460.023.5583.5503.5553.5563.5573.55720.032.8832.8922.9012.9092.9122.89940.052.2712.2682.2392.2472.2572.2564R=100Q0.11.5501.5591.5671.5711.5731.5640.151.3211.3341.3401.3371.3411.33460.21.1411.0801.1581.1291.1131.12420.30.9520.9660.9550.9690.9630.
10、9610.40.7610.7690.7780.7710.7640.76860.50.6980.6990.7460.7500.7050.71960.015.0045.0285.0135.0084.9975.010.023.5753.5553.5603.5653.5673.56440.032.8992.9112.9122.9122.9022.90420.052.2482.2402.2532.2542.2562.2502R=150Q0.11.6021.5941.5971.5901.5861.59380.151.3091.2961.3021.2921.2951.29880.21.1231.1191.1
11、271.1231.1241.12320.30.9170.9250.9340.9200.9120.92160.40.7890.7900.7940.8010.7960.7940.50.7110.7120.7040.7090.7090.70861.3电容取值对RLC并联谐振电路实验误差的影响表 3 并联电路 R 与 C 取不同值时测量的谐振频率的测量值0.015.0015.0775.0615.0174.9845.0280.023.6383.6913.4323.6783.7343.63460.033.1823.2322.9162.9633.1123.0810.052.2742.3082.2022.23
12、52.2542.2546R=OQ0.11.6361.6571.5611.5811.6081.60860.151.3211.3401.2511.2691.2961.29540.21.0541.0701.1611.1771.1151.11540.30.8600.8190.9020.9100.8990.8780.40.5820.5930.6360.6520.6120.6150.50.4680.3010.3070.4570.4720.410.014.8264.9624.9254.8374.8794.8860.023.6193.5513.5923.5673.5923.58420.032.9682.973
13、2.9822.9923.0142.98580.052.4892.5752.5442.4892.4922.5179R=30Q0.11.6261.6461.6201.6351.6481.6350.151.1511.1571.1411.1501.1451.14880.21.1151.1251.1201.1231.1171.120.30.8910.8940.9030.8960.8900.89480.40.8050.8160.8810.8120.8090.81060.50.3250.3300.2370.2330.3240.28980.015.0004.9194.9254.9904.7214.9110.023.6833.7413.6013.5923.6273.64920.033.0063.0222.9162.9233.0102.98740.052.3012.2692.2982.3052.257
