Question

The bridge shown in figure is used to measure the quality factor of coil. Which is represent by a parallel combination of resistance $R_p$ and inductance $L_p$, the bridge is balance at 100 Hz, supply frequency.



Choose the correct statement(s).

• A. The value of unknown resistance $R_p$ is $8.4k\Omega$
• B. The value of unknown inductance $L_p$ is 6.3 mH
• C. The quality factor of coil will be 2122.06
• D. Both $R_p$ and $L_p$ are independent of frequency

Answer 1

Answer: (A), (B), (C), (D)

Both $R_p$ and $L_p$ are independent of frequency

Bridge is balanced at 100 Hz.

At balanced condition,

$\left(\frac{j\omega R_P{L}_P}{R_P+j\omega L_P}\right)\times (R_2+\frac{1}{j\omega C})=R_3{R}_4$

$\Rightarrow j\omega R_P{L}_P.R_2+\frac{R_P{L}_P}{C}=R_3{R}_4{R}_P+j\omega L_P{R}_3{R}_4$

On comparing real and imaginary parts

$R_p=\frac{R_3.R_4}{R_2}=\frac{1.26\times 5\times {10}^5}{75}=8.4l\Omega$

and
$L_p=R_3.R_4.C=1.26\times 5\times {10}^5\times 0.01\times {10}^{-6}=6.3mH$

$\Rightarrow$ The quality factor for this bridge circuit can be given by

$Q_P=\frac{\frac{V_P^2}{X_L}}{V_P^2}{R}_P=\frac{R_P}{\omega L_P}=\frac{8.4\times {10}^3}{200\pi \times 6.3\times {10}^{-3}}=2122.06$

$\Rightarrow Thecoilparameters{R}_{p}and{L}_p,bothareindependentoffrequency.$