Anderson's Bridge is a specific type of electrical circuit used for measuring the self-inductance of a coil, its quality factor, and the frequency of an alternating current (AC) source. It was invented by American physicist Arthur John Arnot Anderson in the late 19th century. The bridge is designed to determine the values of these parameters accurately and efficiently.
The Anderson's Bridge circuit consists of four arms, similar to a Wheatstone bridge. However, the arms contain both resistors and reactive components (inductors and capacitors), making it suitable for AC measurements. The circuit diagram includes the following components:
Ratio Arms (R1 and R2): These are resistors that create a balanced bridge condition by adjusting their values. The ratio of R1 to R2 determines the measurement accuracy.
Inductor (L): The coil whose self-inductance (L) needs to be measured is connected to one of the arms. The inductor introduces a phase difference between the currents in the bridge arms, which plays a crucial role in balancing the bridge.
Capacitor (C): A capacitor is used to balance the reactive effect of the inductor and create a phase shift opposite to that of the inductor.
Variable Resistor (Rv): This resistor is adjusted to fine-tune the balance of the bridge by compensating for the differences in the inductive and capacitive reactances.
AC Source (V): The alternating current source provides the input signal for the bridge circuit.
The primary objective of the Anderson's Bridge is to achieve a balanced condition where the current through the detector (usually a galvanometer) becomes zero. This is accomplished by adjusting the variable resistor (Rv) and the ratio of resistors (R1/R2). When the bridge is balanced, the following conditions are satisfied:
The magnitudes of the inductive and capacitive reactances are equal.
The bridge is in a state of resonance.
From the bridge's balanced condition, it is possible to calculate the self-inductance of the coil (L) and the quality factor (Q) using the following formulas:
Self-inductance (L):
L = R2^2 * C
Quality Factor (Q):
Q = R2 / Rv
By varying the frequency of the AC source and observing the changes in the bridge's balance, one can determine the resonant frequency of the circuit, which is related to the properties of the inductor and capacitor.
Anderson's Bridge is a useful tool in the field of measurement and instrumentation for characterizing electrical components in AC circuits. It provides a method for accurate measurement of inductance and quality factor, both of which are crucial in various electronic applications.