DR. A. O. ADEWALECourse Outline:Electrostatics, potential and capacitance, dielectrics, production and measurement of static electricity. Current, Ohm’s law, resistance and resistivity, heating, Galvanometers, Voltmeters and Ammeters.D.C. circuits, sources of emf and currents, Kirchhoff’s laws. Electrochemistry. The Earth’s magnetic fields and induction. Faraday’s and Lenz’s Laws. Force on a current carrying conductor. Biot-Savart law. Flemmings right and left-hand rules, motors and generators.

Cells in Series and ParallelWhen two or more cells are in series, with the positive

terminal of one connected to the negative terminal of another, then the total e.m.f. is given as,

E = E1 + E2 + E3 +…and the total internal resistance is r = r1 + r2 + r3 +… If one of the cell, say e.m.f. E3, is connected in opposition

with the others, then E = E1 + E2 - E3 +…but the total internal resistance remains unaltered.When similar cells are in parallel, then total e.m.f. = E, the

e.m.f. of any one of them. The internal resistance r is given by

where r1 is the internal resistance of each cell.

...1111

321

rrrr

Example

rREI

E = 1.5 V + 1.5 V = 3.0 V

E = 20 V - 12 V = 8 V

E = 12 V

Current in a typical circuit

rRERIRV

Terminal p.d

ExampleConsider the circuit diagram in Figure 13.15.

Calculate the terminal p.d. across AB.

Class Work

The figure shows a battery of 12 V and negligible internal resistance connected to three resistors. Calculate the p.d. V across the 6 Ω resistor and the current passing through the 8 Ω resistor.

ExampleConsider the circuit diagram in Figure 13.15.

Calculate the terminal p.d. across AB.

Class Work

The figure shows a battery of 12 V and negligible internal resistance connected to three resistors. Calculate the p.d. V across the 6 Ω resistor and the current passing through the 8 Ω resistor.

Practice Questions1. What is the magnitude of a point charge

whose electric field 50 cm away has magnitude 2.0N/C?

2. In a rectangular coordinate system, two positive point charges of magnitude 10-8C each are fixed at the points (0.1, 0) and (-0.1, 0). Find the magnitude of the electric field at point (0.2, 0).

3. What is the magnitude of an electric field in which the force on an electron is equal in magnitude to the weight of an electron?

Practice Questions4. A small object carrying a charge of 5 x 10-9 C

experiences a downward force of 20 x 10-9 N when placed at a certain point in an electric field. What is the electric field at the point?

5. Find the electric field at a point 0.2 m from a charge of 20 C, what force will the field exert on a charge of 10 C, placed at that point?

6. What is the electric field E experienced by a charge of magnitude 5 nC at a point where the electric force is 2 x 10-4 N in the x direction? If an electron is placed in this field, what force will be exerted on it?

Practice Questions7. An oil drop of mass 2 x 10-14 kg carries a

charge of 8 x 10-18 C. The drop is stationary between two parallel plates 20 mm apart with a p.d. of V between them. Calculate V.

8. Two charges q1 = 10 µC and q2 = -12 µC are within a spherical surface of radius 10 cm. What is the total flux through the surface?

9. A charged oil drop of mass 1.0 x 10-14 kg remains stationary when situated between two parallel metal plates 25 mm apart and a p.d. of 1000 V is applied to the plates. Find the charge on the drop.

Practice Questions10. Two plates of a capacitor are 2.50 m

apart while the potential difference between the plates is 72.0 volts. What is the electric field intensity on each of the plate?

11. Find the potential difference required to give a helium nucleus (Q = 3.2 x 10-19C) 48 x 103eV of kinetic energy.

12. Two point charges Q1 = 10C and Q2 = -2C are arranged along the x-axis at x = 0 and x = 4m respectively. Find the positions along the x-axis where V = 0.

Practice Questions13. A 1F and a 2F capacitor are connected in

series across a 1000 volt supply line. Find the charge on each capacitor and the voltage across each.

14. A parallel plate air capacitor is made of 0.2 m square tin plates and 1 cm apart. It is connected to a 50 V battery. What is the charge on each plate?

15. The plates of a parallel-plate capacitor are 2 mm apart and 5 m2 in area. The plates are in vacuum. A potential difference of 2000 volts is applied across the capacitor. Calculate the magnitude of the electric field between the plates.

Practice Questions16. A capacitor of capacitance C is fully charged by a

200 V battery. It is then discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity 2.5 x 102 Jkg-1K-1 and of mass 0.1 kg. If the temperature of the block rises by 0.4 K, what is the value of C?

17. A parallel plate air capacitor is made using two plates 0.2 m2 spaced 1 cm apart. It is connected to a 50 V battery. What is the charge on each plate?

18. The dimensions of plates of a parallel plate capacitor are 8 cm by 8 cm, and they are separated by a distance of 2 mm. Calculate the capacitance if air is between the plates. Calculate also the capacitance if a glass of dielectric constant 5 fills the space between the plates.

Practice Questions19. A 6 F capacitor and a 3 f capacitor are

connected in series across an 18 volts d.c source. Calculate the charge on each capacitor.

20. What area of the plates of a parallel-plate capacitor gives 1 F, if the separation of the plates is 1mm and the plates are in vacuum?

8. Two charges q1 = 10 µC and q2 = -12 µC are within a spherical surface of radius 10 cm. What is the total flux through the surface?

9. A charged oil drop of mass 1.0 x 10-14 kg remains stationary when situated between two parallel metal plates 25 mm apart and a p.d. of 1000 V is applied to the plates. Find the charge on the drop.

15. The plates of a parallel-plate capacitor are 2 mm apart and 5 m2 in area. The plates are in vacuum. A potential difference of 2000 volts is applied across the capacitor. Calculate the magnitude of the electric field between the plates.