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
Maxwell bridge is used to measure
Which method is especially suitable for the measurement of small inductances?
Which of the following method is used for the precise measurement of self and mutual inductance and capacitance of a bridge network with an alternating current supply?
Hay’s bridge is used to measure inductances of coils having:
Megger is a measuring instrument, used for the measurement of:
