Question

Measurement and Instrumentation Theory and Application

Please answer the below question for all parts. Please show all work and write clearly. Thanks. Figure 7.9 and a hint is below.

7.23 An unknown capacitance Cu is measured using a deflection bridge as shown in Figure 7.9. The components of the bridge have the following values: Vs =10Vrms, C1 =50 uF, R2=80 ohms, R3=20 ohms. If the output voltage is 3Vrms, calculate the value of Cu.

2 Zu 3 Vs R2 0 Figure 7.9 Common deflection-type AC bridge.

Answer 1

Given data V_s = 10 V_rms C_1 = 50 mu F R_2 = 80 ohm R_3 = 20 ohm C_u = ? In the hint, they given output voltage V_0 = 3 V_rms i.e. 3 V_rms between the midpoints The voltage between the resistors is 8 V_rms by voltage division. So that the voltage between the capacitors = 3 V_rms. Therefore Voltage division across two capacitors = 10 * Z_1/Z_1 + Z_u = 5 V_rms. \r\n therefore The given figure is c_1 = 50 mu F \r\n Here hint given voltage division still applies for the two capacitors = 10 * Z_1/Z_1 + Z_u = 5 V_rms equation (1) The above equation (1) possible only if Z_1 = Z_u therefore 1/w c_1 = 1/w c_mu c_mu = c_1 c_mu = 50 mu F
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