Explain the worming of Anderson’s bridge with a neat sketch. Derive the required expression for obtaining the unknown inductance.
By using this bridge, the unknown inductance is measured in terms of a known capacitance and resistance.
Let, \(L_1\) = Self-inductance to be measured
\(R_1\) = Resistance of self-inductor
\(C\) = Fixed Capacitor
\(R_1\) = Resistance connected in series with self-inductor
\(R_4, R_3, R_2, r\) = Known non-inductive resistances.
At balance, \(I_1 = I_3\) and \(I_2 = I_C+I_4\)
\(I_1R_3=I_C\times\frac{1}{j\omega C}\)
\(I_C=I_1R_3j\omega C\)
Writing other balance equations,
\(I_1\left(r_1+R_1+j\omega L_1\right)=I_2R_2+I_Cr\) ........(1)
and, \(I_C\left(r+\frac{1}{j\omega C}\right)=\left(I_2-I_C\right)R_4\) .........(2)
Putting the value of \({I}_C\) in equation \(\left(1\right)\), we get,
\(I_1\left(r_1+R_1+j\omega L_1\right)=I_2R_2+I_1R_3j\omega Cr\)
\(I_1\left(r_1+R_1+j\omega L_1-R_3j\omega Cr\right)=I_2R_2\) ........(3)
Putting the value of \(I_C\) in equation (2)
\(I_1R_3j\omega C\left(r+\frac{1}{j\omega C}\right)=\left(I_2-I_1R_3j\omega C\right)R_4\)
\(I_1\left(R_3j\omega Cr+R_3j\omega C R_4+R_3\ \right)=I_2R_4\) .........(4)
From equation (3) & (4) we get,
\(I_1\left(r_1+R_1+j\omega L_1-R_3j\omega Cr\right)=I_1\left(\frac{R_2R_3}{R_4}+\frac{j\omega C R_2R_3r}{R_4}+j\omega C R_2R_3\right)\)
Equating the real and imaginary parts \(R_1=\frac{R_2R_3}{R_4}-r_1\)
\(L_1=c\frac{R_3}{R_4}[r\left(\ R_4+R_2\right)+R_2R_4]\)
What is lissajous pattern? Explain how phase & frequency can be measured using this figures.
Define the terms accuracy, Precision, Resolution, Drift and Relative limiting error.
What are the difference between TED’s and junction device?
Why Schottky diodes are suitable for microwave region?
Compare PAM, PWM and PPM
