- 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 [14]
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: 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: 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.
Definition: Electric Power
In an electrical circuit, electric power is defined as the rate at which electrical energy is supplied by the source.
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: 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: 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: Specific Resistance
Specific resistance of a material is the resistance of a wire of that material of unit length and unit area of cross-section.
S.I. Unit of resistivity is ohm-metre, i.e., Ω·m.
\[\rho=R\left(\frac{A}{l}\right)\]
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 [2]
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: Specific Resistance
- Specific resistance is a characteristic property of a substance and differs among metals, semiconductors, and insulators.
- Specific resistance depends on temperature: it increases with temperature for metals and decreases with temperature for semiconductors, while it remains nearly constant for some alloys.
- Specific resistance does not depend on the shape and size of the conductor and remains unchanged when a wire is stretched or doubled.
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
