Examville.com - Electric Current And Resistance

Electric Current and Resistance 1. There are two types of charges, positive charge and negative charge. 2. Whenever the charge is transferred from one body to another, the total charge is constant throughout, i.e. the charge is conserved. 3. An electric current consists of flow of charged particles in a definite direction. The direction of current flow is generally taken to be in the direction of positive charge flow. (a). In conducting liquids, ions (negative or positive ) are the current carriers. (b). In solid conductors (e.g. metals), free electrons (negative charges) are the current carriers. (c). In gases, free electrons and positive ions are the current carriers. (d). In semiconductors, free electrons and holes (positive charges) are the current carriers. 4. Electric current is a scalar quantity. 5. The magnitude of current is the rate of flow of charge, for a steady current I, I = q/t amperes, where q = charge in C, t = time in seconds When the current is not steady, the instantaneous current I = dq / dt. 6. Conductors which obey ohm’s law i.e. I α V, are called ohmic conductors. (E.g. metals).The V-I graph (V on axis Y-axis, and I on X-axis) is a straight line passing through the origin. The slope of the graph gives the resistance R = V / I, of the conductor. The reciprocal of the slope of the graph gives conductance G = 1 / R of the conductor. 7. Conductors which do not obey ohm’s law (i.e. V / I graph is not a straight line) are called non ohmic conductors E.g. gas discharge tube, junction diode, thermistor etc.

8. The resistance R and conductance G of a conductor are given by R = ρ (l / A) and G = 1/R = (1/ρ) (A / l) = σ(A / l) Where σ = 1 / ρ = electrical conductivity. The unit of G is siemen(S) and that of σ is Sm-1 or Ω-1m-1. Resistance (R) as well as conductance (G) of a conductor depends upon (a). The length (l), (b). The area of cross section (A) (c). Nature of material of the conductor (d). Temperature of the conductor. 9. Free electron density (n) in a metal is given by n = NAxd / M Where NA = Avogadro’s number, x = No. of free electrons per atom, d = density of metal, M = atomic mass of metal 10. The relation between current I flowing through a conductor and drift velocity vd of free electrons is I = neAvd Where n = free electrons density i.e. number of free electrons per unit volume A = area of x – section of conductor E = charge on each electron Vd = drift velocity of free electrons As n, e, A are constant, I α vd. 11. Current density (J) at a given point in a conductor is the current per unit area at that point i.e. area normal to current. Its unit is Am-2. J = I/A = (neAvd) / A = nevd 12. The resistance of pure metals and metallic alloys increases with increase in temperature and vice versa. However the resistance of insulators and semiconductors decreases with increase in temperature and vice versa.

13. When wire is drawn under pressure, its length increases and diameter decreases. However the volume of the wire remains the same before and after drawing. 14. The temperature coefficient of resistance α is given by, α = (Increase in resistance per 0C) / (Resistance at 00C) For any conductor, the value of α depends on temperature but the variation is slight. So, average value of α between t10C and t20C (where t2>t1) is given by Α = (R2 – R1) / R1 (t2 – t1) Where R1 and R2 are the resistances of the conductor at t10C and t20C respectively. So, R2 = R1 {1 + α (t2 – t1)} 15. When n equal resistors, each of resistance R are connected in series, the equivalent resistance Rs = nR. When these resistors are connected in parallel, the equivalent resistance Rp = R / n. So, Rs / Rp = nR / (R/n) = n2 16. When two resistances R1 and R2 are connected in parallel, the equivalent resistance Rp is given by Rp = (R1R2) / (R1 + R2) = Product / Sum Current through R1 = I1 = Total current x (other resistance / Sum) = I x {R2 / (R1 + R2)} Current through R2 = I2 = Total current x (other resistance / sum) = I x {R1 / (R1+R2)} 17. When the cell is delivering no current, the potential difference across the terminals of the cell is equal to e.m.f. of the cell.

18. When a cell of e.m.f E and internal resistance r is delivering current I to an external resistance R, then E = V + Ir = IR + Ir = I (R + r) Where, V is terminal voltage. 19. Cells may be connected in three ways to form a battery (i). Series grouping (ii). Parallel grouping (iii). Series- parallel grouping 20. If n cells each of e.m.f E and internal resistance r are connected in series across an external resistance R, then total e.m.f = nE and total circuit resistance = R + nr, where nr = internal resistance of the battery. So, circuit current, I = (Total e.m.f.) / (Total circuit resistance) = nE / (R + nr) That’s why to get maximum current in a series grouping of cells, the external resistance R should be very large in comparison to the internal resistance of the battery nr. 21. If x rows of cells, each row containing one cell of e.m.f. E and internal resistance r are connected in parallel across an external resistance R, then the total e.m.f = E and total circuit resistance = R + r/x, where r/x = internal resistance of the battery. So, circuit current I = (Total e.m.f.) / (Total circuit resistance) = E / {R + (r/x)} = xE / (xR + r) To get maximum current in parallel grouping of cells, the external resistance R should be very small as compared to the internal resistance of each call. 22. If x no. cells, each of e.m.f. E and internal resistance r are connected in series and n such rows are connected in parallel across an internal resistance

R, then total e.m.f. = xE. The resistance of x series connected cells = xr. So, internal resistance rT of the battery is (1/rT) = (1/xr) + (1/xr) + …….n times = n/xr = xr/n Total resistance = R + (xr/n) Circuit current I = nE / {R + (xr/n)} = nxE / (nR + xr) To get maximum current in this series – parallel grouping of cells, the external resistance R should be equal to the total internal resistance of the battery (xr/n). 23. If a battery is receiving current I (i.e. if it is being charged), then terminal voltage V is V = E + ir Where E = battery e.m.f. and r = internal resistance of the battery. 24. The internal resistance of a lead-acid cell is very low. 25. When unlike cells are connected in parallel, Kirchoff’s laws have to be used to solve the problem. ******************************************