---
title: "Maxwell bridge balance equation and suitability"
subject: "Instrumentation I"
chapter: 2
key: "semester_4/instrumentation_i:maxwell-bridge-inductance"
source: https://www.bctengineer.com/q/semester_4/instrumentation_i/maxwell-bridge-inductance
site: BCT Engineering
---

# Maxwell bridge balance equation and suitability

Instrumentation I · Chapter 2: Theory of measurement

- Asked in: year not given, 8 marks
- Video: [Maxwell inductance bridge | maxwell inductance bridge in hindi | maxwell inductance bridge formula](https://www.youtube.com/watch?v=jotDW4zYRfI) — Mind of Engineer 
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/instrumentation_i/maxwell-bridge-inductance
- Whole chapter: https://www.bctengineer.com/md/semester_4/instrumentation_i/chapter-2

## Question

Obtain the balance equation for Maxwell bridge and explain why it is suitable for the measurement of inductance of coil having quality factor between 1 to 10.

## Short answer

Maxwell bridge balance gives R1 = R2R3/R4, L1 = R2R3C4, Q = ωC4R4. It is suitable for Q 1–10 because R4 and C4 have practical values. For high Q, R4 becomes too large; for very low Q, balance adjustments interact, causing convergence problems.

## Answer

The **Maxwell inductance-capacitance bridge** measures an unknown inductance by comparing it with a standard capacitor.

#### Circuit
```text
          A
        /   \
  L1,R1(Z1)  R3 (Z4)
      /         \
     B---[D]----D
      \         /
    R2 (Z2)   R4 || C4 (Z3)
        \     /
          C
```
Arm AB: unknown coil (L1, R1). BC: R2. CD: R4 in parallel with a standard capacitor C4. DA: R3.

#### Balance equation
Using Z1 Z3 = Z2 Z4, with Z3 = R4/(1 + jωC4R4):

(R1 + jωL1) · R4/(1 + jωC4R4) = R2R3

(R1 + jωL1) R4 = R2R3 + jωC4R2R3R4

Real parts: **R1 = R2 R3 / R4**

Imaginary parts: **L1 = R2 R3 C4**

Quality factor: **Q = ωL1/R1 = ωC4R4**

Both results are independent of frequency. If R4 and C4 are the variable elements, the two balance conditions are independent (R4 sets R1 and C4 sets L1).

#### Why it is suitable for Q between 1 and 10
- Q = ωC4R4. For Q up to about 10, R4 and C4 have reasonable values, so a standard decade resistor and a standard capacitor can be used.
- For Q > 10 (high-Q coils), R4 would have to be very large; such resistors are expensive and inaccurate and suffer from stray effects, so the Hay bridge is used instead.
- For Q < 1 (very low Q), the bridge has balance-convergence problems. In practice C4 is fixed (a variable standard capacitor is costly), so R3 (or R2) and R4 are adjusted; R3 appears in both balance equations, so the adjustments interact. With low Q this causes a "sliding balance", and many alternate adjustments are needed to reach the null.
- Only a standard capacitor is needed, which is cheaper, smaller and more accurate than a standard inductor, and the balance is independent of frequency.
- Disadvantage: the range of Q covered is limited; the bridge is not suitable for high-Q or very low-Q coils.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. At balance of the Maxwell bridge, the unknown inductance is:
   A. L1 = R2 R3 C4
   B. L1 = R2 R3 / R4
   C. L1 = R2 R3 R4
   D. L1 = C4 R4 / R2
   Answer: A. Equating imaginary parts gives L1 = R2R3C4; real parts give R1 = R2R3/R4. (Key point: Maxwell balance results)

2. In the Maxwell bridge the coil's quality factor is:
   A. 1/(omega C4 R4)
   B. omega C4 R4
   C. R2R3/R4
   D. omega L1 R4
   Answer: B. Q = omega L1/R1 = omega C4 R4. (Key point: Q of the coil)

3. Why is the Maxwell bridge unsuitable for coils with Q > 10?
   A. R4 would need to be very large, which is expensive and inaccurate
   B. The balance depends on frequency
   C. It needs a standard inductor
   D. C4 would be zero
   Answer: A. Since Q = omega C4 R4, high Q needs a very large R4 with stray effects; the Hay bridge is used instead. (Key point: Why not high Q)

4. Which is an advantage of the Maxwell bridge?
   A. It needs a standard inductor
   B. Balance depends on frequency
   C. It is best for very high Q
   D. It uses a standard capacitor and balance is frequency independent
   Answer: D. A standard capacitor is cheaper and more accurate than a standard inductor, and the results contain no frequency term. (Key point: Advantage)

## Related in Instrumentation I

- [Bridge for high-Q inductance measurement](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_i%3Ahigh-q-inductance-bridge) — Instrumentation I, chapter 2
- [AC bridge balance and Schering bridge](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_i%3Aschering-bridge-capacitance) — Instrumentation I, chapter 2

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