Consider an AC bridge shown in the figure with $R=300\Omega$, $R1=1000 \Omega$, $R2=500 \Omega$, $L=30mH$, and a detector D. At the bridge balance condition, the frequency of the excitation source $V_s$ is _________ kHz (rounded off to two decimal places).
To find the frequency at which the AC bridge is balanced, we use the balance condition of an AC bridge:
Complex impedance in opposite arms are equal.
Given:
\(R = 300 \, \Omega\), \(R_1 = 1000 \, \Omega\), \(R_2 = 500 \, \Omega\), \(L = 30 \, \text{mH}\)
The balance condition for the bridge is:
\(\dfrac{R_1}{R_2} = \dfrac{R}{j\omega L}\)
Where \(\omega = 2\pi f\)
\(f = \dfrac{R}{2\pi L} \cdot \dfrac{1}{1 + \dfrac{jR_2}{R_1}}\)
Simplifying, we get:
\(f = \dfrac{R \cdot R_1}{2\pi L \cdot R_2}\)
Plug in values:
\(f = \dfrac{300 \times 1000}{2\pi \times 30 \times 10^{-3} \times 500}\)
\(f = \dfrac{300000}{94.248}\)
\(f \approx 1591.55 \, \text{Hz} = 1.59 \, \text{kHz}\)
The frequency is \(1.59 \, \text{kHz}\), which is within the range of \(1.55 \, \text{kHz}\) to \(1.65 \, \text{kHz}\).
Important Questions from Measurement of R/L/C Using Bridge Circuits
Megger is a measuring instrument, used for the measurement of:
Which of the following bridges is used to measure dielectric loss and capacitance of dielectric material?
In which of the following, vibration galvanometer, tuneable amplifier and headphones are used?
How much accuracy can be obtained using Wien’s bridge?
Maxwell bridge is used to measure
