Wheatstone Bridge — Revision Notes

⚡ 30-Second Revision

Wheatstone Bridge Principle — Used for precise unknown resistance measurement.
Balanced Condition — $I_g = 0$ (no current through galvanometer), $V_B = V_D$.
Formula for Balance — $\frac{P}{Q} = \frac{R}{S}$
Meter Bridge Formula — $\frac{R_{left}}{R_{right}} = \frac{l_1}{100-l_1}$ (without end corrections)
End Corrections — Add small values to $l_1$ and $l_2$ for precision: $\frac{R_{left}}{R_{right}} = \frac{l_1+x}{l_2+y}$
Interchangeability — Battery and galvanometer can be interchanged without affecting the balanced condition.
Unbalanced Bridge — Analyze using Kirchhoff's Laws; current flows from higher to lower potential.

2-Minute Revision

The Wheatstone bridge is a critical circuit for accurately measuring unknown resistances using a null detection method. It consists of four resistors (P, Q, R, S) in a bridge configuration. A galvanometer is connected across two points, and a battery across the other two.

The bridge is 'balanced' when the galvanometer shows zero deflection, meaning no current flows through it. At this point, the potentials at the galvanometer's connection points are equal, leading to the fundamental balanced condition: $P/Q = R/S$.

This allows for precise calculation of an unknown resistance if three others are known. The Meter Bridge is a practical form of the Wheatstone bridge, using a uniform resistance wire. Its balance condition is $R_{left}/R_{right} = l_1/(100-l_1)$, where $l_1$ is the null point length.

Remember to consider end corrections for higher accuracy. The balanced condition is independent of the battery's internal resistance or interchanging the battery and galvanometer. For unbalanced bridges, current flows from higher to lower potential, requiring potential calculations.

5-Minute Revision

The Wheatstone bridge is an indispensable tool in electrical measurements, primarily for determining an unknown resistance with high precision. Its core strength lies in the 'null method' – it seeks a zero reading on a galvanometer, which is inherently more accurate than measuring a non-zero value.

The circuit comprises four resistors, typically labeled P, Q, R, and S, forming a closed loop. A voltage source is applied across one diagonal, and a galvanometer across the other. When the bridge is balanced, the galvanometer registers no current ($I_g = 0$), implying that the electrical potentials at its two connection points are identical ($V_B = V_D$).

This leads to the crucial balanced condition: $\frac{P}{Q} = \frac{R}{S}$. If, for instance, S is the unknown resistance, it can be calculated as $S = R \times \frac{Q}{P}$.

Meter Bridge Application: A common laboratory setup, the Meter Bridge, is a direct application. Here, two arms of the bridge are formed by segments of a uniform resistance wire. If an unknown resistance $R_X$ is in the left gap and a known resistance $R_K$ in the right, and the null point is found at length $l_1$ from the left end, then the balance condition becomes $\frac{R_X}{R_K} = \frac{l_1}{100-l_1}$.

For precise measurements, 'end corrections' (small additions to $l_1$ and $100-l_1$) must be applied to account for contact resistances. For example, if $R_X$ is unknown and $R_K = 10\,\Omega$, and the null point is at $60\,\text{cm}$, then $R_X/10 = 60/40 = 3/2$, so $R_X = 15\,\Omega$.

Key Points for NEET:

1
Balanced vs. Unbalanced — Understand the distinction. Only for balanced bridges does $P/Q = R/S$ apply. For unbalanced bridges, Kirchhoff's laws are needed, and current flows from higher to lower potential.
2
Reciprocity — The balanced condition remains unchanged if the battery and galvanometer are interchanged.
3
Sensitivity — The bridge is most sensitive when all four resistances are of comparable magnitude.
4
Circuit Recognition — Be able to identify Wheatstone bridge configurations in complex circuits; if balanced, the central resistor can be removed for simplification. Practice problems involving series/parallel combinations within the bridge arms.

Prelims Revision Notes

Wheatstone Bridge: Quick Recall for NEET

1. Basic Circuit & Principle:

Four resistors (P, Q, R, S) in a diamond shape.
Battery across one diagonal (e.g., A to C).
Galvanometer (G) across the other diagonal (e.g., B to D).
Principle: — Null deflection method – adjust resistances until galvanometer shows zero current ($I_g = 0$).

2. Balanced Condition:

When $I_g = 0$, the potential at B equals potential at D ($V_B = V_D$).
Formula: — $\frac{P}{Q} = \frac{R}{S}$ (or $\frac{P}{R} = \frac{Q}{S}$).
This allows calculation of an unknown resistance if three are known.

3. Meter Bridge (Slide Wire Bridge):

A practical application of Wheatstone bridge.
Uses a 1-meter uniform resistance wire as two arms.
Setup: — Unknown resistance ($R_X$) in one gap, known resistance ($R_K$) in the other.
Null Point: — Found by sliding a jockey on the wire at length $l_1$ from one end.
Formula: — $\frac{R_X}{R_K} = \frac{l_1}{100-l_1}$ (if $R_X$ is in the gap corresponding to $l_1$).
End Corrections: — For higher accuracy, small lengths ($x, y$) are added to measured lengths due to contact resistance: $\frac{R_X}{R_K} = \frac{l_1+x}{(100-l_1)+y}$.

4. Key Conceptual Points:

Null Method Advantage: — High accuracy as it relies on detecting zero, not measuring a value.
Galvanometer Role: — Acts as a null detector, not a current meter. Its internal resistance is irrelevant when balanced.
Interchangeability: — The balanced condition ($P/Q = R/S$) remains unchanged if the battery and galvanometer are swapped. Sensitivity might change.
Unbalanced Bridge: — $P/Q \neq R/S$. Current flows through the galvanometer. Analysis requires Kirchhoff's Laws. Current direction is from higher potential to lower potential (e.g., if $V_B > V_D$, current flows B to D).
Sensitivity: — Bridge is most sensitive when all four resistances are comparable in magnitude.

5. Problem-Solving Tips:

Identify the bridge configuration, even if it's not standard.
Apply the balanced condition directly for unknown resistance or null point.
Remember series/parallel combinations if resistors are grouped in the arms.
Don't forget end corrections if specified in meter bridge problems.
For unbalanced bridges, calculate potentials at the galvanometer points to find current direction.