NIOS Final Exam Focus
Lesson 16: Electric Potential and Capacitors
This chapter usually gives direct theory questions, derivations, and capacitor numericals. Revise definitions, formulas, and comparisons carefully.
1. Electric Potential
- Electric potential at a point is the work done in bringing a unit positive charge from infinity to that point.
- Potential is a scalar quantity.
- SI unit of potential is volt (V).
- Potential difference is work done per unit charge between two points.
- Work done in electrostatic field is path independent.
V = W/q and VB - VA = WAB/q
2. Potential due to Point Charge
- Potential due to a point charge varies as 1/r.
- For positive charge, potential is positive.
- For negative charge, potential is negative.
- If many charges are present, total potential is algebraic sum, not vector sum.
V = (1/4πε0) (q/r)
3. Potential due to Electric Dipole
- Potential due to dipole depends on distance and angle.
- It varies as 1/r2.
- On axial line, potential is maximum in magnitude.
- On equatorial line, potential is zero.
V = (1/4πε0) (p cos θ/r2)
4. Equipotential Surfaces
- All points on an equipotential surface have same potential.
- No work is done in moving a charge on an equipotential surface.
- Electric field is always perpendicular to the equipotential surface.
- Two equipotential surfaces never intersect.
5. Potential Energy
- Potential energy of a system is the work done in assembling charges from infinity.
- For like charges, potential energy is positive.
- For unlike charges, potential energy is negative.
- For a dipole in uniform electric field, potential energy depends on angle.
U = (1/4πε0) (q1q2/r), U = -pE cos θ
6. Relation Between Electric Field and Potential
- Electric field is equal to negative potential gradient.
- Negative sign shows potential decreases in the direction of electric field.
- If potential is constant in a region, electric field is zero there.
E = -dV/dr and for uniform field E = (VA - VB)/d
7. Conductors in Electrostatic Equilibrium
- Electric field inside a conductor is zero.
- Any excess charge resides on the outer surface.
- Electric field at the surface is perpendicular to the conductor.
- Cavity inside a conductor is shielded from external electric field.
- This is the basis of electrostatic shielding.
8. Capacitance
- A capacitor stores charge and electrical energy.
- Capacitance is the ratio of charge to potential difference.
- SI unit is farad (F).
- Capacitance depends on size, shape, and medium, not on material alone.
C = Q/V
9. Important Capacitor Formulas
- Capacitance of isolated spherical conductor is directly proportional to radius.
- For parallel plate capacitor, capacitance increases with plate area and decreases with separation.
- If dielectric is inserted, capacitance increases by factor K.
Sphere: C = 4πε0r
Parallel plate: C0 = ε0A/d
With dielectric: C = Kε0A/d = KC0
10. Dielectric Constant
- Relative permittivity or dielectric constant is denoted by K or εr.
- It compares a medium with vacuum.
- It can be expressed using force or capacitance ratio.
K = ε/ε0 = Fvac/Fmedium = C/C0
11. Grouping of Capacitors
- In parallel, potential difference is same across each capacitor.
- In parallel, equivalent capacitance is greater than each individual capacitance.
- In series, charge is same on each capacitor.
- In series, equivalent capacitance is less than the smallest capacitor.
Parallel: Cp = C1 + C2 + C3 + ...
Series: 1/Cs = 1/C1 + 1/C2 + 1/C3 + ...
12. Energy Stored in a Capacitor
- Charging a capacitor requires work.
- This work is stored as electrostatic potential energy.
- Energy increases with capacitance and with square of potential difference.
U = (1/2)CV2 = (1/2)QV = Q2/(2C)
13. Dielectric Polarization
- Non-polar dielectrics have no permanent dipole moment in normal state.
- Polar dielectrics already have permanent dipole moment.
- In external electric field, dielectric gets polarized.
- Polarization creates an opposing field inside dielectric.
- Effective field decreases, so capacitance increases.
Eeffective = E - Ep
14. NIOS Exam Traps
- Potential is scalar, electric field is vector.
- Potential can be zero while electric field is not zero, for example on equatorial line of a dipole.
- If electric field is zero in a region, potential may be zero or constant.
- For capacitors in series, same charge; for parallel, same potential difference.
- Insertion of dielectric usually increases capacitance.
15. High-Value Questions to Prepare
- Derivation of potential due to a point charge.
- Derivation of capacitance of parallel plate capacitor.
- Series and parallel combination of capacitors.
- Energy stored in a capacitor.
- Electrostatic shielding and behavior of conductors in electric field.
- Effect of dielectric on capacitance.
Best revision method: learn one formula with meaning, unit, and one line about where it is used.