Wheatstone Bridge Notes 🔗

1. The Basic Setup 💡

A Wheatstone bridge has four resistors—R1, R2, R3, and R4—arranged in a diamond. A power source connects points A and C (the battery arm), while a sensitive galvanometer G joins points B and D (the galvanometer arm). If the cell is ideal (no internal resistance), currents flow through every branch along with a possible galvanometer current Ig. :contentReference[oaicite:0]{index=0}

2. Balanced Bridge Condition 🟢

The bridge is balanced when the galvanometer reads zero (Ig = 0). Kirchhoff’s current rule gives I1 = I3 and I2 = I4. Applying the loop rule then yields the famous balance equation:

\( R_2\,R_4 = R_1\,R_3 \)    (Eq. 3.64 a)

When this relation is met, the bridge shows null deflection—no current through the galvanometer. :contentReference[oaicite:1]{index=1}

3. Finding an Unknown Resistance 📏

Place the unknown resistor in the fourth arm (R4). Keep R1 and R2 fixed, vary R3 until the galvanometer again reads zero, and then use

\( R_4 = \dfrac{R_2\,R_3}{R_1} \)    (Eq. 3.64 b)

A classroom favorite called the meter bridge is a direct, one-meter-long implementation of this idea, letting you slide a contact to adjust R3 smoothly until balance is achieved. :contentReference[oaicite:2]{index=2}

4. Worked Example 📝

  • Bridge arms: AB = 100 Ω, BC = 10 Ω, CD = 5 Ω, DA = 60 Ω. A 15 Ω galvanometer connects B and D.
  • With 10 V across AC, mesh equations give a galvanometer current Ig ≈ 4.87 mA.

5. High-Yield NEET Nuggets 🚀

  1. Balance trick: \( R_2\,R_4 = R_1\,R_3 \) ensures Ig=0. :contentReference[oaicite:3]{index=3}
  2. Unknown resistor formula: \( R_4 = \dfrac{R_2\,R_3}{R_1} \). :contentReference[oaicite:4]{index=4}
  3. Meter bridge magic: A one-meter wire bridge lets you vary R3 continuously for quick balancing. :contentReference[oaicite:5]{index=5}
  4. Null deflection: Zero galvanometer current protects the instrument and boosts accuracy. :contentReference[oaicite:6]{index=6}

6. Quick Recap 😃

Remember: Balance the bridge, note the null point, and plug numbers into the neat little formulas above. Practicing a few setups on a meter bridge will make these ideas second nature—happy experimenting! ✨