# Electric Measurment

Kirchhoff’s Laws:

In 1845, a German physicist, Gustav Kirchhoff, developed a pair of laws that deal with the conservation of current and energy within electrical circuits. These two laws are commonly known as Kirchhoff’s Voltage and Current Law.

Kirchhoff’s Current Law

According to Kirchhoff’s Current Law,

The total current entering a junction or a node is equal to the charge leaving the node as no charge is lost.

This property of Kirchhoff law is commonly called conservation of charge, wherein I(exit) + I(enter) = 0.

This can be expressed in the form of an equation:

I1 + I2 + I3 – I4 – I5 = 0

Note: A node refers to a junction connecting two or more current-carrying routes like cables and other components.

Kirchhoff’s Voltage Law

According to Kirchhoff’s Voltage Law,

The voltage around a loop equals the sum of every voltage drop in the same loop for any closed network and equals zero.

Or

The algebraic sum of every voltage in the loop has to be equal to zero and this property of Kirchhoff’s law is called conservation of energy.

Wheatstone bridge Principle:

Principle:

The Wheatstone bridge works on the principle of null deflection, i.e. the ratio of their resistances is equal, and no current flows through the circuit.

Important Condition:

The bridge is in an unbalanced condition where current flows through the galvanometer. The bridge is said to be balanced when no current flows through the galvanometer. This condition can be achieved by adjusting the known resistance and variable resistance.

## Wheatstone Bridge Derivation

The current enters the galvanometer and divides into two equal magnitude currents as I1 and I2. The following condition exists when the current through a galvanometer is zero,

Wheatstone Bridge Formula

Following is the formula used for the Wheatstone bridge:

Where,

R is the unknown resistance

S is the standard arm of the bridge

P and Q is the ratio of the arm of the bridge

Wheatstone Bridge Application

« It is used for the precise measurement of low resistance.

« Wheatstone bridge and an operational amplifier are used to measure physical parameters such as temperature, light, and strain.

« Quantities such as impedance, inductance, and capacitance can be measured using variations on the Wheatstone bridge.

Wheatstone Bridge Limitations

« For low resistance measurement, the resistance of the leads and contacts becomes significant and introduces an error.

« For high resistance measurement, the measurement presented by the bridge is so large that the galvanometer is insensitive to imbalance.

« The resistance change due to the current’s heating effect through the resistance. Excessive current may even cause a permanent change in the value of resistance

Meter Bridge

A meter bridge, also called a slide wire bridge, is an instrument that works on the principle of a Wheatstone bridge. A meter bridge is used to find the unknown resistance of a conductor as that of in a Wheatstone bridge.

Then according to Wheatstone’s principle, we have:

The unknown resistance can be calculated as:

Then the specific resistance of the material of the is calculated as:

Where,

L is the length of the wire

r is the radius of the wire

Potentiometer

The potentiometer is an instrument used to measure the unknown voltage by comparing it with the known voltage. It can be used to determine the emf and internal resistance of the given cell and also used to compare the emf of different cells. The comparative method is used by the potentiometer.

Working Principle of Potentiometer

The basic principle of the potentiometer is that the potential drop across any section of the wire will be directly proportional to the length of the wire, provided the wire is of a uniform cross-sectional area and a uniform current flows through the wire.

To Determine the EMF of the Cell (Calibration)

Let ‘i’ be the current flowing through the wire.

i = ɛ/(r+R)

Here,

ɛ is the emf of the cell in the primary circuit

r is the internal resistance

R is the resistance of the wire

The voltage across the potentiometer wire of length

L is taken as

VAB = V0

The fall of potential per unit length of the potentiometer wire is called the potential gradient.

Z = (V0/L) is the potential gradient.

The jockey is moved on the wire, and the null point (P) is determined. The point on the wire is called the null point when the galvanometer will not show any deflection. The length of the wire AP is taken as ‘l’.

The potential difference between A and P will be

⇒VA – VP = (V0/L).l

= Z.l = Ɛ’ (since V0 = iR)

Ɛ’ is the emf of the cell connected in the secondary circuit.

Heating Effect of Current

The English physicist James Prescott discovered that the amount of heat per second that develops in a current-carrying conductor is proportional to the electrical resistance of the wire and the square of the current.

Joule’s Law of Heating:

Joule’s law is a mathematical description of the rate at which resistance in a circuit converts electric energy into heat energy

Q = ${I}^{2}$R T

Where,

Q indicates the amount of heat

I show electric current

R is the amount of electric resistance in the conductor

T denotes time