Current Electricity Notes

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CHAPTER – 13                                                                                         CURRENT ELECTRICITY

Qs. 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

Qs. 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.

Electrostatics and Current Electricity MCQs with Answers

Qs. 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

Qs. 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)

Qs. 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

Qs. 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