Question

A Maxwell's inductance-capacitance bridge is used to measure an unknown inductive impedance. The bridge constants at bridge baiance are Pure resistance arms =2.5kh and 50kQ.

In between these two resistors, the third arm has a capacitor of value 0.012 uf in series with a resistor of value 235kn.
Find the series equivalent of the unknown impedance.

Answer 1

To find the unknown series impedance in a Maxwell's inductance-capacitance bridge, you must apply the bridge balance equation which equates the product of the impedances on one diagonal to that on the other diagonal. Given the values for the resistors and capacitor in the circuit, the unknown impedance can be calculated.

Step-by-step explanation:

To calculate the equivalent series impedance of an unknown inductive impedance using a Maxwell's inductance-capacitance bridge, we use the bridge balance condition. The bridge balance equation for this bridge is given by:

Z_1 * Z_4 = Z_2 * Z_3

Where Z_1 is the unknown impedance we are trying to find, Z_2 and Z_4 are the pure resistances, and Z_3 is the impedance of the capacitor in series with a resistor.

Given:

• Z_2 = 2.5 kΩ
• Z_4 = 50 kΩ
• Z_3 = 235 kΩ + 1/(j2πfC) where C = 0.012 μF

The unknown Z_1 can be calculated by rearranging the balance equation:

Z_1 = (Z_2 * Z_3) / Z_4

It is important to remember that the impedance Z_3 is composed of a resistive and a capacitive part, which means you have to take into account the contribution of both the resistance and the reactance of the capacitor at the frequency of the bridge's operation.