- Heating Effect: Current through a resistor produces heat, calculated by H = I²Rt or H = VIt (Joule’s Law).
- Heat Applications: Used in devices like irons, heaters, bulbs, and fuses (to stop excess current).
- Power Unit: 1 kWh = 3.6 × 10⁶ J, called 1 unit of electrical energy in electricity bills.
- Short Circuit & Fuse: A short circuit causes a large current; the fuse wire melts to break the circuit and prevent fire.
- MCBs: Miniature Circuit Breakers automatically cut off power during overload or fault conditions.
Definitions [23]
Definition: Mobility
It is defined as the magnitude of the drift velocity of the charge carriers per unit electric field.
\[\mu=\frac{v_d}{E}=\frac{e\tau}{m}\]
The S.I. unit of mobility is \[\mathrm{m^{2}s^{-1}~V^{-1}}\] or \[\mathrm{ms^{-1}N^{-1}C}\]
Definition: Electric Current
Electric current is defined as the amount of electric charges flowing through any cross-section of a conductor per unit time.
\[I=\frac{\text{Total charge flowing (Q)}}{\text{Time taken (t)}}\]
\[I=\frac{Q}{t}\]
The S.I. unit of current is ampere (A)
Definition: Ampere
Electric current through a conductor is said to be one ampere if charge of one coulomb flows through any cross-section of the conductor in one second.
\[1\mathrm{~ampere~(A)}=\frac{1\mathrm{~coulomb~(C)}}{1\mathrm{~second~(s)}}=1\mathrm{~C~s}^{-1}\]
Definition: Drift Velocity
It is defined as the velocity with which the free electrons are drifted towards the positive terminal under the effect of the applied electric field.
- The drift velocity of electrons is given by \[v_d=\frac{eE\tau}{m}\]
Definition: Conductivity
Conductivity, denoted by σ, measures how easily current flows through a material. From the microscopic model, conductivity depends on free electron density and relaxation time.
Definition: Drift Velocity
The average velocity acquired by free electrons in a conductor under the influence of an electric field is called the drift velocity.
Definition: Relaxation Time
The average time interval between two successive collisions of a free electron with the ions of the metallic lattice is called the relaxation time and is denoted by τ.
Definition: Current Density
Current density is the current flowing per unit cross-sectional area of the conductor. The source material connects current density with the drift motion of electrons.
Definition: Ohmic Device
A device that obeys Ohm's law and gives a straight-line V-I graph through the origin.
Definition: Non-ohmic Device
A device that does not obey Ohm's law and shows a non-linear or direction-dependent V-I relation.
Definition: Resistivity
Resistivity, denoted by ρ, is the intrinsic property of a material that determines how much it resists current flow.
Definition: Temperature Coefficient of Resistivity
The temperature coefficient of resistivity, denoted by α, measures the fractional change in resistivity per degree change in temperature in the linear range.
- Unit: per degree Celsius or per kelvin.
- For metals, α > 0.
- For semiconductors, α < 0.
Definition: Electrical Energy
The electrical energy consumed in a circuit is defined as the total work done in maintaining the current in the electric circuit for a given time.
Electrical Energy = \[VIt=I^2Rt=\frac{V^2t}{R}\]
S.I. unit of electric energy is joule (1 kWh = \[3.6\times10^6\mathrm{~J}\])
Define Electric power.
Electric power (P) is the rate at which electrical energy is transferred or consumed in an electrical circuit.
What does the unit kilowatt hour measure? Define it.
The unit kilowatt-hour measures electrical energy. 1 kWh is the electrical energy consumed by an electric appliance of power 1 kW when it is used for 1 hour.
Definition: Electric Power
In an electrical circuit, electric power is defined as the rate at which electrical energy is supplied by the source.
Definition: Terminal Potential Difference (V)
When current is drawn through a cell or current is supplied to it, then the potential difference across its terminals is called the terminal potential difference.
\[V=E-Ir\]
Definition: EMF of a Cell
The emf of a cell is defined as the work done in carrying a unit positive charge through the complete circuit, including the charge flow inside the cell.
Unit: J/C (or) volt
Definition: Internal Resistance of a Cell
The resistance offered by the electrolyte of the cell when an electric current flows through it is known as internal resistance.
Definition: Electrical Resistivity
Electrical Resistivity (ρ) is defined as the resistance offered by a conductor of unit length and unit cross-sectional area at a given temperature. It is a characteristic property of the material, independent of its dimensions.
Define fuse.
Electric fuse is a safety device which is used in household wiring and in many appliances.
Define the following:
Electrolyte
The solution through which the electricity passes is called an electrolyte.
Definition: Heating effect of electric current
When a resistor is connected in an electrical circuit, heat is produced in it due to the current. This is known as the heating effect of current.
Formulae [5]
Formula: Drift Velocity
Using the average time between collisions τ, the source derives the drift velocity as:
vd = −\[\frac {eEτ}{m}\]
Formula: Resistivity at temperature T
ρT = ρ0[1 + α(T − T0)]
Here:
- ρT = resistivity at temperature T.
- ρ0 = resistivity at reference temperature T0.
- α = temperature coefficient of resistivity.
Formula: Resistance at Changed Temperature
RT = R0(1 + αΔT)
where ΔT = T − T0.
Formula: Electric Power
Electric Power P = \[\frac {W}{t}\] = VI = \[\frac {V^2}{R}\] = I2R
Write the mathematical expression for Joule’s law of heating.
The mathematical expression of Joule’s Law of heating is: H = I2 Rt
Where,
H = Produced Heat
I = Current flowing through the device
t = Time taken
r = Resistance of the appliance
Key Points
Key Points: Temperature Dependence of Resistance
Resistivity and Temperature:
\[\rho_T=\rho_0[1+\alpha(T-T_0)]\]
Resistance and Temperature:
\[R_T=R_0(1+\alpha\Delta T)\]
Temperature Coefficient (α):
- Unit: °C⁻¹ (or K⁻¹)
- Metals: α > 0→ resistivity increases with temperature
Semiconductors & insulators:
α < 0 → resistivity decreases with temperature
Key Points: Electric Power
- Electrical power represents the rate at which electrical energy is supplied by the source in an electric circuit.
- The S.I. unit of electrical power is a watt (W), and larger units such as kilowatt, megawatt, and gigawatt are used for measuring higher power.
Key Points: Parallel Combination of Resistors
- In parallel, resistors are connected across the same two points (multiple paths).
- Voltage is the same across all resistors.
Equivalent resistance:
\[\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\cdots\]
For n identical resistors:
Req = R/n
Current relation:
I = I₁ + I₂ + I₃
Current divider rule:
I₁ : I₂ : I₃ = \[\frac{1}{R_{1}}:\frac{1}{R_{2}}:\frac{1}{R_{3}}\]
Req < Rmin
Key Points: Cells in Series
- Cells are connected from the positive terminal to the negative terminal.
- Total emf is the sum of individual emfs:
Enet = E₁ + E₂ + E₃ + ... - Total internal resistance:
rnet = r₁ + r₂ + r₃ + ... - For n identical cells:
Enet = nE
rnet = nr - Current in the circuit:
\[I=\frac{E_{\mathrm{net}}}{r_{\mathrm{net}}+R}\] - For identical cells:
\[I=\frac{nE}{nr+R}\]
Key Points: Heating Effect of Electric Current
Concepts [15]
- Electric Current and Its Related Concepts
- Drift of Electrons and the Origin of Resistivity
- Limitations of Ohm’s Law
- Resistivity of Various Materials
- Temperature Dependence of Resistivity
- Forms of Energy > Electrical Energy
- Electrical Power
- Resistors in Parallel
- Cells, EMF, and Internal Resistance
- V-I Characteristics (Linear and Non-linear)
- Specific Resistance or Electrical Resistivity
- Resistivity of Various Materials
- Cells in Series
- Heating Effect of Electric Current
- Cells, Thermo e.m.f. Electrolysis
