XII Physics BIEK Chapter 13 - Current Electricity

CURRENT ELECTRICITY
Define Charge and Current.

CHARGE
Definition

Flow of electron is known as Charge.

It is denoted by Q.


Unit

Its unit is Coulomb.

1 Coulomb = 10(-6) μcoulomb

1 coulomb = 10 (-3) mili coulomb

1 coulomb = 10(-9) neno coulomb




CURRENT
Definition

The flow of charge per unit time is known as Current.

It is denoted by I.


Unit

The unit of current is coulomb/sec or Ampere.




AMPERE
If one coulomb charge passes through the conductor in 1 second then the current is 1 Ampere.


Mathematical Form

Mathematically,

I = Q/t


State and Explain Ohm's Law.

OHM'S LAW
Introduction

A German scientist George Simon Ohm studied the relationship between voltage, current and resistance. On the basis of his experimental results, he proposed a law which is known as Ohm's Law.


Statement

Ohm's Law to metallic conductors can be stated as

The current through a conductor is directly proportional to the potential difference between the ends of the conductor provided that physical conditions are kept constant.

It can also be stated as

The ratio between voltage and current remains constant, if the physical conditions are kept constant.


Mathematical Form

Mathematically,

V ∞ I

V = IR

R = V/I

Where R is the constant of proportionality known as resistance of the conductor. Its unit is volt per ampere (Volt/Ampere) or Ohm (Ω).


Ohm (Ω)

If 1 ampere current passes through the conductor due to 1 volt potential difference then the resistance of conductor is 1 Ohm.


Resistance

Opposition offered in the flow of current.


Graphical Representation.

When graph is plotted between current and potential differences then straight line is obtained.


Limitations of the Law

Ohm's Law is valid only for metallic resistance at a given temperature and for steady currents.


Define the term Resistivity or Coefficient of Resistor.

RESISTIVITY OR COEFFICIENT OF RESISTOR
Definition

It is the resistance of a unit conductor whose cross-sectional area is 1 sqm.


Unit

Its unit is Ohm meter.


Mathematical Form

The resistance of any conductor depends upon the following factors.

1. Length of the conductor

2. Cross-sectional area of the conductor.

3. Material of the conductor.

The resistance of the conductor is directly proportional to the length of the conductor and inversely proportional to the cross-sectional area.

Mathematically,

R ∞ L -------- (I)

R α 1/A ------ (II)

Combining eq (I) and (II)

R α L/A

=> R = ρL/A

Where ρ is the constant of proportionality known as Resistivity or Coefficient of resistance.

ρ = RA/L


Explain the effect of temperature on resistance or temperature coefficient of resistance.

EFFECT OF TEMPERATURE ON RESISTANCE
It is observed that if we increase the temperature then resistance of a conductor will increase.


Consideration

Let Ro be the initial resistance of a conductor at 4°C. If we increase the temperature from t1°C to t2°C, then resistance will increase. This increment in resistance is denoted by ΔR. The increment in resistance depends upon the following two factors.

1. Original Resistance (Ro)

2. Difference in temperature Δt.


Mathematical Verification

The increment in resistance is directly proportional to the original resistance and temperature difference.

Mathematically,

ΔR ∞ Ro ----- (I)

ΔR ∞ Δt ----- (II)

Combining eq (I) and eq (II) we get

ΔR ∞ RoΔt

=> ΔR = αRoΔt

Where α is the temperature coefficient of resistance. It is defined as

It is the increment in resistance per unit resistance per degree rise in temperature.

Its unit is 1/°C or °C. If RT is the total resistance, then

RT = Ro + ΔR

=> RT = Ro + αRo Δt

=> RT = Ro (1 + αΔt)

As we know that resistance is directly proportional to resistivity therefore,

ρT = ρo (1 + αΔt)


Define the term Power Decipation in Resistor.




POWER DECIPATION IN RESISTORS
Definition

When current flows in a conductor then a part of electrical energy appears in the form of heat energy which is known as Power Decipation in Resistor.


Units

Its unit is Joule per second (J/s). Most commonly used unit is Kwh.

1 Kwh = 36 x 10(5) Joules


Mathematical Form

Since,

P = Electrical Work / Time

Electrical Work = QV ------ (I)

This electrical work produces heat energy in the resistor.

P = QV / t

P = Q / t . V

But,

I = Q / t

P = VI

From Ohm's Law

V = IR

P = IIR

P = I2R

OR,

P = 12R2 / R

=> P = V2 / R

As we know that,

Energy = Power x time


=> E = P x t

=> E = Vit

=> E = I2Rt

And,

E = V2 / R . t
Define and explain Electromotive Force.

ELECTROMOTIVE FORCE
Definition

It is the terminal voltage difference when no current draws from a cell or a battery.

OR

Work done per coulomb on the charges.

It is denoted by E.


Unit

Electromotive force or simply e.m.f is a scalar quantity it has the same dimension as that of voltage, therefore its unit is volt.


Explanation

When an electric current passes through a resistor, it dissipates energy, which is transformed into heat energy. Thus to sustain a current in conductor some source of energy is needed so that it could continuously supply power equal to that which is dissipated as heat in the resistor. The strength of this source is called Electromotive Force.


Consideration

Let consider a simple circuit in which a resistor "R" is connected by leads of negligible resistance to the terminals of a battery. The battery is made up of some electrolyte and electrode for the production of e.m.f and hence when this current flows from battery, it encounters some resistance by the electrolyte present in two electrodes. This resistance is known as internal resistance "r" of the battery.

Mathematical Form

According to Ohm's Law

V = IR

I = V / R

Or,

I = E / R + r

Where E is e.m.f and r is internal resistance

=> E = IR + Ir

E = V + Ir