The Maxwell Bridge is shown in the figure below. It measures an unknown inductance in terms of a known capacitance. The unknown inductance with its resistance is represented as L_{X} and R_{X} respectively. The parallel combination of the variable resistance R_{1} and the capacitor C_{1} forms a ratio arm. A variable resistance R_{3} and resistance R_{2} take the positions of the two other arms of the bridges.

Taking Z

_{x}= Z_{2}Z_{3}Y_{1}
Z

_{2}= R_{2}
Z

_{3}= R_{3}
Y

_{1}= 1/R_{1}+ jωC_{1}
Therefore Z

_{x}= R_{x}+ jωL_{x}= R_{2}R_{3}(Y_{1})
= R

_{x}+ jωL_{x}= R_{2}R_{3}(1/R_{1}– jωC_{1})
= R

_{x}+ jωL_{x}= ((R_{2}R_{3})/R_{1}) + R_{2}R_{3}jωC_{1}
Equating real terms:

R

_{x}= R_{2}R_{3}/R_{1}
Equating imaginary terms:

L

_{x}= R_{2}R_{3}C_{1}
Hence we have two variables R

_{1}and C_{1}that appear in one of the two balance equations and hence the two equations are independent. The expression for Q factor:
Q = ωL

_{x}/R_{1}= ωC_{1}R_{1}The Maxwell Bridge Advantages and Disadvantages are as follows.

**(a) Advantages of Maxwell Bridge:**

1. The two balance equations are independent if we chose R

_{1}and C_{1}as variable elements.
2. The frequency does not appear in any of the two equations.

3. This bridge gives simple expression for unknown values of L

_{x}and R_{x}in terms of known bridge elements. Physically R_{2}and R_{3}can be each say 10, 100, 1000 or 10,000 Ω. and their value is selected to give suitable value of product R_{2}R_{3}that appears in both the balance equations. C_{1}can be a decade capacitor and R_{1}can be a decade resistor. If the product R_{2}R_{3}= 10^{6}, then the inductance is given by
L

_{x}= C_{1}x 10^{6}.
Therefore when the balance is achieved the value of C

_{1}directly in micro-farads gives the value of inductance in henry.
4. This bridge is useful for measurement of wide range of inductance at power and audio frequencies.

**(b) Disadvantages of Maxwell Bridge :**

1. The bridge requires a variable standard capacitor which can be very costly if the degree of accuracy is high. In some cases fixed value of capacitance are used. The balance adjustment may be done by either varying R

_{2}or R_{1}. As R_{2}appears in both the balance equations, the balance adjustment will be difficult. Other method is to place extra resistance in series with the inductance under measurement and then varying the resistance R_{1}.
2. This bridge can measure values of inductance of medium Q coils. The reason is that the phase angles of arms 2 and 3 put together must be equal to the phase angles of arms 1 and 4 added up and that must be equal to 0°.

To accommodate the measurement of high Q coil the phase angle of the capacitive arm must be nearly 90° (negative), as the phase angle of a high Q coil will be nearly 90°. This needs a very large value of resistance R

_{1}which is practically not possible.
Low Q coils also cannot be measured with this bridge due to the interaction of R

_{1}and R_{3}. When R_{3}is adjusted for inductive balance, the resistive balance is upset. This is termed sliding balance. That is when once balanced with R_{1}and then with R_{3}if we try to balance again with R_{1}we get new balance point. The balance appears to be moving or sliding towards the final point after several adjustments. Therefore this bridge is to be balanced first with R_{3}for inductance balance and then with R_{1}for resistive balance. The process is to be repeated to get the final balance.
Hence we note that this Maxwell bridge is suitable for measuring medium Q coils alone.

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