Topics
Electric Charges and Fields
- Electric Charge
- Conductors and Insulators
- Basic Properties of Electric Charge
- Coulomb’s Law
- Forces between Multiple Charges
- Electric Field
- Electric Field Due to a System of Charges
- Physical Significance of Electric Field
- Electric Field Lines
- Electric Flux
- Electric Dipole
- Dipole in a Uniform External Field
- Continuous Charge Distribution
- Gauss’s Law
- Application of Gauss' Law
Electrostatics
Electrostatic Potential and Capacitance
- Electric Potential and Potential Energy
- Electrostatic Potential
- Electric Potential Due to a Point Charge
- Potential Due to an Electric Dipole
- Potential due to a System of Charges
- Equipotential Surfaces
- Relation Between Electric Field and Electrostatic Potential
- Potential Energy of a System of Charges
- Potential Energy of a Single Charge
- Potential Energy of a System of Two Charges in an External Field
- Potential Energy of a Dipole in an External Field
- Electrostatics of Conductors
- Dielectrics and Polarisation
- Capacitors and Capacitance
- The Parallel Plate Capacitor
- Effect of Dielectric on Capacitance
- Combination of Capacitors
- Energy Stored in a Charged Capacitor
Current Electricity
Magnetic Effects of Current and Magnetism
Current Electricity
- Electric Current
- Electric Currents in Conductors
- Ohm's Law
- Drift of Electrons and the Origin of Resistivity
- Mobility of Electrons
- Limitations of Ohm’s Law
- Resistivity of Various Materials
- Temperature Dependence of Resistivity
- Electrical Energy and Power in Conductors
- Cells, EMF, and Internal Resistance
- Cells in Series and in Parallel
- Kirchhoff’s Laws
- Wheatstone Bridge
Electromagnetic Induction and Alternating Currents
Moving Charges and Magnetism
- Electromagnetism
- Magnetic force
- Motion in a Magnetic Field
- Magnetic Field Due to a Current Element, Biot-savart Law
- Magnetic Field on the Axis of a Circular Current-Carrying Loop
- Ampere’s Circuital Law
- Solenoid
- Force Between Two Parallel Currents (Ampere’s Law)
- Torque on a Rectangular Current Loop in a Uniform Magnetic Field
- Circular Current Loop as a Magnetic Dipole
- Moving Coil Galvanometer
- Kirchhoff’s Laws
Magnetism and Matter
Electromagnetic Waves
Optics
Electromagnetic Induction
Alternating Current
Dual Nature of Radiation and Matter
Atoms and Nuclei
Electromagnetic Waves
Electronic Devices
Ray Optics and Optical Instruments
- Ray Optics Or Geometrical Optics
- Reflection of Light by Spherical Mirrors
- Sign Convention for Reflection by Spherical Mirrors
- Focal Length of Spherical Mirrors
- Mirror Equation of Spherical Mirrors
- Refraction of Light
- Total Internal Reflection
- Applications of Total Internal Reflection
- Refraction at a Spherical Surfaces
- Refraction by a Lens
- Power of a Lens
- Combined Focal Length of Two Thin Lenses in Contact
- Refraction of Light Through a Prism
- Optical Instruments
- Microscope and it’s types
- Telescope
- Overview of Ray Optics and Optical Instruments
Wave Optics
- Concept of Wave Optics
- Huygens Principle
- Refraction of a Plane Wave
- Refraction at a Rarer Medium
- Reflection of a Plane Wave by a Plane Surface
- Coherent and Incoherent Addition of Waves
- Interference of Light Waves and Young’s Experiment
- Diffraction of Light
- The Single Slit
- Seeing the Single Slit Diffraction Pattern
- Polarisation of Light
- Overview: Wave Optics
Communication Systems
Dual Nature of Radiation and Matter
- Understanding Dual Nature of Radiation and Matter
- Electron Emission
- Photoelectric Effect - Hertz’s Observations
- Photoelectric Effect - Hallwachs’ and Lenard’s Observations
- Experimental Study of Photoelectric Effect
- Effects of Intensity and Frequency on Photocurrent
- Photoelectric Effect and Wave Theory of Light
- Einstein’s Photoelectric Equation: Energy Quantum of Radiation
- Particle Nature of Light: The Photon
- Wave Nature of Matter
- Overview: Dual Nature of Radiation and Matter
The Special Theory of Relativity
Atoms
Nuclei
- Atomic Masses and Composition of Nucleus
- Size of the Nucleus
- Mass - Energy
- Nuclear Binding Energy
- Nuclear Force
- Radioactivity
- Forms of Energy > Nuclear Energy
- Nuclear Fission
- Nuclear Fusion
- Controlled Thermonuclear Fusion
- Overview: Nuclei
Semiconductor Electronics - Materials, Devices and Simple Circuits
- Concept of Semiconductor Electronics
- Classification of Metals, Conductors and Semiconductors
- Intrinsic Semiconductor
- Extrinsic Semiconductor
- n-type Semiconductor
- p-type Semiconductor
- Diode or p-n Junction
- Semiconductor Diode
- Application of Junction Diode as a Rectifier
- Overview: Semiconductor Electronics
Communication Systems
- Detection of Amplitude Modulated Wave
- Production of Amplitude Modulated Wave
- Basic Terminology Used in Electronic Communication Systems
- Sinusoidal Waves
- Modulation and Its Necessity
- Amplitude Modulation (AM)
- Need for Modulation and Demodulation
- Satellite Communication
- Propagation of EM Waves
- Bandwidth of Transmission Medium
- Bandwidth of Signals
The Special Theory of Relativity
- The Special Theory of Relativity
- The Principle of Relativity
- Maxwell'S Laws
- Kinematical Consequences
- Dynamics at Large Velocity
- Energy and Momentum
- The Ultimate Speed
- Twin Paradox
Estimated time: 8 minutes
CBSE: Class 12
Introduction
A resistor R, inductor L, and capacitor C are connected in series with an AC (alternating current) source.
Key Property
Since all three elements are in series, the same AC current flows through each of them. This current has the same amplitude and same phase throughout the circuit.
The instantaneous current in the circuit is written as:
i = im sin (ωt + ϕ) ...(1)
where:
- im = peak (maximum) amplitude of current
- ω = angular frequency of the AC source
- ϕ = phase difference between the applied voltage and the current
CBSE: Class 12
Phasors and Voltage Relationships
The circuit is analysed using phasors — rotating vectors that represent sinusoidal quantities.
The phasors involved are: I (current), VR, VL, VC, and V (applied voltage).
Phase Relationships Between Voltage and Current
| Component | Voltage Phasor | Phase Relation with Current |
|---|---|---|
| Resistor (R) | \[V_R\] | Voltage is in phase with the current (\[\phi = 0^\circ\]). |
| Capacitor (C) | \[V_C\] | Voltage lags the current by \[\dfrac{\pi}{2}\] (90°). |
| Inductor (L) | \[V_L\] | Voltage leads the current by \[\dfrac{\pi}{2}\] (90°). |
CBSE: Class 12
Voltage Amplitudes
The peak (amplitude) of voltage across each element is:
VRm = imR ...(2)
VCm = imXC ...(3)
VLm = imXL ...(4)
where XC and XL are the capacitive reactance and inductive reactance, respectively.
CBSE: Class 12
Phasor Sum (KVL in Phasor Form)
By Kirchhoff's Voltage Law, the phasors of the three voltages must add up to the applied voltage phasor:
VL + VR + VC = V ...(5)
This is a phasor (vector) sum, not an algebraic sum. The voltages are at different phases and cannot be added directly as numbers.
CBSE: Class 12
Derivation of Impedance and Phase Angle
Using the right-angle triangle formed in the phasor diagram:
From the right-angle phasor triangle:
\[v_m^2=V_{Rm}^2+(V_{Cm}-V_{Lm})^2=(i_mR)^2+(i_mX_C-i_mX_L)^2\]
\[v_m=i_m\sqrt{R^2+(X_C-X_L)^2}\]
Therefore, the peak current is:
\[{i_m=\frac{v_m}{Z}}\] ...(6)
where Impedance Z is defined as:
\[{Z=\sqrt{R^{2}+(X_{C}-X_{L})^{2}}}\] ...(7)
Phase Angle φ
From the phasor triangle, the phase angle between the applied voltage and current is:
\[{\tan\phi=\frac{X_C-X_L}{R}}\] ...(8)
CBSE: Class 12
Phase Conditions
Depending on the relative magnitudes of XC and XL, the circuit behaves differently.
| Condition | Circuit Nature | Behaviour |
|---|---|---|
| \[X_C > X_L\] | Predominantly Capacitive | Current leads the voltage (\[\phi > 0)\]. |
| \[X_C < X_L\] | Predominantly Inductive | Current lags the voltage (\[\phi < 0)\]. |
| \[X_C = X_L\] | Resonance | Current and voltage are in phase (\[\phi = 0)\]. |
CBSE: Class 12
Steady-State vs. Transient Solution
The phasor method gives only the steady-state solution of the circuit — the long-term sinusoidal behaviour after the circuit has settled.
The complete solution is:
Complete Solution = Transient Response + Steady-State (Phasor) Solution
The transient response appears when the circuit is first switched on, but it dies out over time, leaving only the steady-state behaviour.
