EXPERIMENT- 4 Anderson’s Bridge

BIMT

Aim

Measurement of Inductance by Anderson’s Bridge.

Material Required

Anderson Bridge Trainer Kit, Wires

Theory

The Anderson bridge is a bridge circuit used for measuring unknown resistances, especially those with high values. The bridge is balanced when the ratio of the resistances in the adjacent arms is equal.

Circuit Diagram

Circuit Diagram Placeholder

Formula used and derivation –

At balance,

$ I_1 (R_1 + j\omega L_1) = I_2 R_2 + I_c R_5 \tag{1} $

$ I_2 = I_3 + I_c \tag{2} $

$ I_3 = \frac{I_c}{R_3} \left( R_5 - \frac{j}{\omega C} \right) \tag{3} $

Putting (3) in (2), we get

$ I_2 = \frac{I_c}{R_3} \left( R_5 - \frac{j}{\omega C} \right) + I_c \tag{4} $

Putting value of $I_2$ from (4) in (1), we get

$ I_1 (R_1 + j\omega L_1) = I_c \left[ R_5 + R_2 + \frac{R_5 R_2}{R_3} - \frac{j R_2}{\omega C R_3} \right] \tag{5} $

Also,

$ I_1 R_1 = I_c \left( - \frac{j}{\omega C} \right) \tag{6} $

Dividing (5) and (6), we get

$ (R_1 + j\omega L_1) \left( - \frac{j}{\omega C} \right) = R_1 \left[ R_5 + R_2 + \frac{R_5 R_2}{R_3} - \frac{j R_2}{\omega C R_3} \right] $

Multiplying and equating real and imaginary parts, we get

$ R_1 = \frac{R_2 R_4}{R_3} $

$ L_1 = C R_4 \left[ R_5 + R_2 + \frac{R_5 R_2}{R_3} \right] $

Procedure

DC BALANCE

  1. Connect DC Supply with the terminals marked supply, unknown inductance with the terminals marked unknown, and a galvanometer with the terminals marked detector.
  2. Now adjust the decade resistance dial R to find out the balance point in the galvanometer and also use resistance dial S for fine adjustment.
  3. Note the value R.

AC BALANCE

  1. After DC Balance without disturbing the position of the bridge, connect the AC Supply 1kHz instead of DC Supply and head phone instead of galvanometer.
  2. Now adjust the resistance dial R to minimize the sound in the head phones.
  3. Note the value of R and calculate the value of unknown inductance by using the given formula.
  4. Repeat the experiment with another value of C.

Observation Table

Combination 1:-

S.No. L C R (in Ω) r (in Ω) P (in Ω) Q (in Ω)
1
2

Repeat for other combinations.

Precautions

  • Make sure all the connections are tight.
  • To avoid inductive effect short straight wires should be used.