IEMDaily - Video Lecture Notes

Definition

Internal resistance using potentiometer

We can also use a potentiometer to measure internal resistance of a cell. For this the cell (emf

E

) whose internal resistance (

r

) is to be determined is connected across a resistance box through a key

K_{2}

. With key

K_{2}

open, balance is obtained at length

l_{1}

(A N_{1})

. Then,

E = ϕ l_{1}

When key

K_{2}

is closed, the cell sends a current (

I

) through the resistance box (

R

). If

V

is the terminal potential difference of the cell and balance is obtained at length

l_{2} (A N_{2})

V = ϕ l_{2}

so,

\frac{E}{V} = \frac{l_{1}}{l_{2}} = \frac{I (r + R)}{I R}

\Rightarrow r = R (\frac{l_{1}}{l_{2}} - 1)

which is the internal resistance of the given cell.

Definition

Precautions while using a potentiometer

1. Jockey should not be dragged along the wire.2. The current value should be as small as possible.3. Current should be passed only while taking the readings.

Definition

Potentiometer vs voltmeter

Voltmeter	Potentiometer
A voltmeter cannot be used to measure the emf of a cell because a voltmeter draws some current from the cell.	To measure a cell's emf a potentiometer is used since in a potentiometer measurement no current is flowing.
Measures emf of cell approximately	Measures emf of cell very accurately
Sensitivity is low	Sensitivity is high

Definition

Relation between resistance and temperature

\frac{Δ R}{R_{0}} = α Δ T

where

R_{0}

is the initial resistance and

α

is the coefficient of thermal expansion. Change in temperature

Δ T

brings about a change in the resistance

Δ R

Definition

Dynamic resistance

Dynamic resistance is used to quantify the resistance of non-ohmic materials. It is defined as the ratio of differential change in voltage to a differential change in current.

r = \frac{d V}{d I}

Note:
Dynamic resistance is itself a function of the current (or voltage) through the material for a non-ohmic conductor.

Definition

Rheostat as a current controller

The electrical component rheostat, have 3 terminals. Two terminals are the begining and end of the wire(

T_{1}

and

T_{2}

), while the 3rd terminal is the movable contact which can be moved along the length of the wire(

T_{3}

).Now by using two terminals(One of them

T_{3}

), Rheostat functions as a current limiter. The value of current flow depends on the resistance in its path, so by adjusting the contact the value of resistance exhibited can be altered thus the current flow can be controlled.
This can accomplished in two ways:In Shunt or in Series.

Definition

Rheostat as a potential divider

A rheostat is a resistance element with considerable length. It is usually metallic in nature. The defining equation is

R = ρ \frac{l}{A}

Where;

ρ =

resistivity of the element.

l =

length of the wire.

A =

area of cross section of the wire.
The electrical component rheostat, have 3 terminals,two terminals are the begining and end of the wire (

T_{1}

and

T_{2}

), while the 3rd terminal is the movable contact which can be moved along the length of the wire(

T_{3}

ρ

and

A

remains the same throughout; thus the resistance between terminals is decided by the length of wire between them.
The length

T_{1}

T_{3}

l_{1}

while

T_{3}

T_{2}

l_{2}

. This results in two resistances

R_{1}

and

R_{2}

; causing an equivalent circuit.By adding a voltage source across

T_{1}

and

T_{2}

; desired voltage can be obtained across

T_{3}

and ground by tuning the point of contact C on the rheostat.

Definition

Meter bridge

A meter bridge consists of a wire of length

1 m

and of uniform cross-sectional area stretched taut and clamped between two thick metallic strips bent at right angles with two gaps across which resistors are to be connected. The end points where the wire is clamped are connected to a cell through a key. One end of a galvanometer is connected to the metallic strip midway between the two gaps. The other end of the galvanometer is connected to a jockey which moves along the wire to make electrical connection.