11.15 The Null Method of Measurement | Electricity | Physics 11

The Null Method is a high-accuracy measurement technique used to determine an unknown quantity by comparing it against a known standard. Instead of measuring the unknown value directly, the method involves adjusting a variable component until a sensitive indicator device reads zero, or "null." This null condition signifies that the unknown quantity is perfectly balanced against the known standard.

Two classic electrical circuits that utilize this principle are the Wheatstone Bridge and the Potentiometer.

1. The Wheatstone Bridge

The Wheatstone Bridge is a circuit designed to precisely measure an unknown electrical resistance. It consists of a diamond-shaped network of four resistors and a sensitive current detector called a galvanometer.

Working Principle

The circuit has two parallel branches. Three of the resistors ( $P$ , $Q$ , $S$ ) have known values, and one ( $R$ ) is the unknown resistance.
A galvanometer is connected between points b and d.
The value of one of the known resistors (often a variable resistor, $S$ ) is adjusted until the galvanometer shows zero current flow.
This "null" reading indicates that points b and d are at the same electric potential, and the bridge is said to be balanced.

Figure 1: Circuit diagram of a Wheatstone Bridge.

Balance Condition Equation

When the bridge is balanced, the ratio of resistances in one branch is equal to the ratio in the other branch: $\frac{P}{Q} = \frac{R}{S}$

From this, the unknown resistance ( $R$ ) can be calculated with high precision: $R = S (\frac{P}{Q})$

2. The Potentiometer

A potentiometer is a versatile instrument used for the precise measurement of potential differences (voltages) without drawing any current from the circuit being measured.

Precision and Accuracy→

Principle and Construction

Principle: It operates on the principle that for a wire of uniform cross-section and composition, the potential drop across any length of the wire is directly proportional to that length.
Construction: It consists of a long, uniform resistance wire stretched between two terminals, a standard driving cell, a galvanometer, and a movable contact called a jockey.

Figure 2: Circuit diagram of a potentiometer.

Applications of the Potentiometer

a) Comparing EMFs of Two Cells

The potentiometer can compare the electromotive forces (EMFs) of two cells, $ε_{1}$ and $ε_{2}$ .
The jockey is moved along the wire for each cell until the galvanometer reads zero. The lengths at which this null point is found ( $l_{1}$ and $l_{2}$ ) are recorded.
The ratio of the EMFs is equal to the ratio of the balancing lengths: $\frac{ε _{1}}{ε _{2}} = \frac{l _{1}}{l _{2}}$

b) Measuring the Internal Resistance of a Cell

The potentiometer can also be used to find the internal resistance ( $r$ ) of a cell.
First, the balancing length ( $l_{1}$ ) is found for the cell's EMF ( $ε$ ).
Then, a known external resistance ( $R$ ) is connected across the cell, and a new, shorter balancing length ( $l_{2}$ ) is found for its terminal potential difference ( $V$ ).
The internal resistance is calculated using the formula: $r = R (\frac{l _{1} - l _{2}}{l _{2}})$

Possible Questions

Q: Why is the null method generally more accurate than direct measurement methods?

A: Null methods are more accurate because they do not depend on the calibration or precision of the measurement device itself (like a voltmeter or ammeter). The accuracy depends only on the precision of the known standard components (like the standard resistors in a Wheatstone bridge). Furthermore, at the null point, no current is drawn from the circuit being measured, so the measurement does not disturb the circuit's original state.

1. The Wheatstone Bridge

The circuit has two parallel branches. Three of the resistors (

P

Q

S

) have known values, and one (

R

) is the unknown resistance.

A galvanometer is connected between points b and d.

The value of one of the known resistors (often a variable resistor,

S

) is adjusted until the galvanometer shows zero current flow.

This "null" reading indicates that points b and d are at the same electric potential, and the bridge is said to be balanced.

Figure 1: Circuit diagram of a Wheatstone Bridge.

When the bridge is balanced, the ratio of resistances in one branch is equal to the ratio in the other branch:

\frac{P}{Q} = \frac{R}{S}

From this, the unknown resistance (

R

) can be calculated with high precision:

R = S (\frac{P}{Q})

2. The Potentiometer

A potentiometer is a versatile instrument used for the precise measurement of potential differences (voltages) without drawing any current from the circuit being measured.

Principle: It operates on the principle that for a wire of uniform cross-section and composition, the potential drop across any length of the wire is directly proportional to that length.

Construction: It consists of a long, uniform resistance wire stretched between two terminals, a standard driving cell, a galvanometer, and a movable contact called a jockey.

Figure 2: Circuit diagram of a potentiometer.

The potentiometer can compare the electromotive forces (EMFs) of two cells,

ε_{1}

and

ε_{2}

The jockey is moved along the wire for each cell until the galvanometer reads zero. The lengths at which this null point is found (

l_{1}

and

l_{2}

) are recorded.

The ratio of the EMFs is equal to the ratio of the balancing lengths:

\frac{ε _{1}}{ε _{2}} = \frac{l _{1}}{l _{2}}

The potentiometer can also be used to find the internal resistance (

r

) of a cell.

First, the balancing length (

l_{1}

) is found for the cell's EMF (

ε

Then, a known external resistance (

R

) is connected across the cell, and a new, shorter balancing length (

l_{2}

) is found for its terminal potential difference (

V

The internal resistance is calculated using the formula:

r = R (\frac{l _{1} - l _{2}}{l _{2}})

Possible Questions

Q: Why is the null method generally more accurate than direct measurement methods?