The ac bridge shown in Fig. 9.84 is known as a Maxwell bridge and is used for accurate measurement of inductance and resistance of a coil in terms of a standard capacitance Cs. Show that when the bridge is balanced,
Lx = R2R3Cs and
Find Lx and Rx for R1 = 40 kΩ, R2 = 1.6 kΩ, R3 = 4 kΩ, and Cs = 0.45 μF.
Figure 9.84
Show that when the bridge in Figure 9.85 is balanced the value of resistor
Answer to Problem 84P
The value of resistor
Explanation of Solution
Given data:
Refer to Figure 9.85 in the textbook.
The value of resistor
The value of resistor
The value of resistor
The value of capacitor
Formula used:
Write a general expression to calculate the impedance of a resistor.
Here,
Write a general expression to calculate the impedance of an inductor.
Here,
Write a general expression to calculate the impedance of a capacitor.
Here,
Calculation:
The given circuit is redrawn as shown in Figure 1.
Use equation (1) to find
Use equation (2) to find
Use equation (3) to find
Now, the impedance diagram of Figure 1 is drawn as shown in Figure 2.
Refer to Figure 2, the impedance of resistor
Therefore, the equivalent impedance
Refer to Figure 2, the impedance of resistor
The equivalent impedance
Let,
The balance of equation of an ac bridge is,
Substitute
Equate the real and imaginary part in above equation.
Simplify the equation (5) to find
Substitute
Substitute
Conclusion:
Thus, when the bridge is balanced, the value of resistor
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Chapter 9 Solutions
Fundamentals of Electric Circuits
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- Delmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage Learning