Hay’s bridge is suitable for inductances having low L/R ratio.
A. True
B. False
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Answer: B
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Explanation:
Hay’s bridge is an AC bridge used for the measurement of self-inductance. It is a modified version of the Maxwell’s inductance bridge where the Maxwell’s bridge’s variable resistor is replaced with a variable capacitor. This modification introduces a frequency-dependant component into the measurement circuit.
Let’s break down the elements of Hay’s Bridge:
R1 is the resistance of the resistor in the first arm.
R2 is the resistance of the resistor in the second arm.
R3 is the resistance of the resistor in the third arm.
R4 is the resistance of the inductor (coil) whose inductance (L4) is being measured.
C4 is a variable capacitor, placed parallel to the inductor.
In Hay’s Bridge, balance condition (when no current flows through the detector D) is given by:
R1 / R2 = R3 / (R4 + 1 / ω^2C4L4)
where ω is the angular frequency (ω = 2πf).
From the equation, it can be seen that for the bridge to balance, the denominator of the right-hand side must not be zero, i.e., the inductor must have a resistance (R4).
When we talk about the L/R ratio, it refers to the ratio of the inductance (L4) to the resistance (R4) of the inductor. In applications with low L/R ratios, the resistance of the inductor becomes significant compared to its inductance.
For Hay’s Bridge, it’s more suited for high L/R ratios. This is because, in the low L/R ratio situation, the term 1 / ω^2C4L4 can become significant relative to R4, causing a large phase shift, making it hard to achieve balance, and introducing errors in the measurement of the inductance L4.
On the other hand, in the high L/R ratio situation, the term 1 / ω^2C4L4 can be neglected relative to R4 (since R4 is small), simplifying the balance condition and making it easier to achieve balance, thus improving the accuracy of the measurement of L4.
Therefore, the statement “Hay’s bridge is suitable for inductances having low L/R ratio” is false. Hay’s bridge is more suited for inductances having high L/R ratio.