
This chapter is about current and potential difference, resistance, electromotive force (e.m.f) and internal resistance and also electrical energy and power.


3.1 
Current and Potential Difference 



Electric field 


The region around a charged particle where any electric charge in the region will experience an electric force 








The patterns of observed electric fields for positive charge and negative charge are as follows:

(a) 
The direction of the electric force line avoids the positive charge.



(b) 
The direction of the electric force line to negative charge.







Electric field strength, E 


Electric force acting on a unit positive charge placed at the point.






\(E=\dfrac{F}{q}\), where E = electric field strength, F = electric force, Q = quantity of electric charge 





\(E=\dfrac{V}{d}\), where E = electric field strength, V = potential difference, d = distance between plates










Electric current, \(I\) 


Rate of flow of charge in a conductor 





\(I = \dfrac{Q}{t}\), \(I\) = current, Q = total charge, t = time 









Potential difference 


Work done in moving one coulomb of charge from one point to another. 





\(V = \dfrac{W}{Q}\) or \(V=\dfrac{E}{Q}\), where V= potential difference, W = work done, E = energy transferred, Q = amount of charges flowing 












Ohm's law 


Potential difference flowing through a conductor is directly proportional to the electric current when the temperature and other physical properties are kept constant.
\(V = I\times R\)








If Ohm's law is obeyed, the graph against it or otherwise is a straight line as follows:



Ohmic conductor 


Conductor which obeys Ohm's Law (Resistance constant)
Example: Constantan wire









Nonohmic conductor 


Conductor which does not obeys Ohm's Law (Resistance constant)
Example: Filament bulb
















Resistance of wire 


\(R=\dfrac{\rho\,l}{A}\) 







Factors that affect the resistance of a wire

 Length of wire, \(l\)
 \(l\) increase, \(R\) increase
 cross sectional area of wire, \(A\)
 \(A\) increase, \(R\) decrease
 resistivity of the wire, \(\rho\)
 \(\rho\) increase, \(R\) increase




Resistivity of a conductor, \(\rho\) 


 a measure of a conductor's ability to oppose the flow of electric current
 unit is ohmmeter
 depends on the temperature and the nature of the conductor material









3.3 
Electromotive Force (e.m.f) and Internal Resistance 



Electromotive force, \(\varepsilon\) 


Energy transferred or work done by an electrical source to move one coulomb of charge in a complete circuit.
\(\varepsilon=\dfrac{E}{Q}\), where, \(\varepsilon\) = electromotive force, E = energy transferred / work done, Q = the amount of charge flowing










Internal resistance, r 


Resistance caused by electrolyte in the dry cell.
\(\varepsilon > V\)
\(Ir = \varepsilon  V\)









Formula relating E, V, I, R and r 


 \(\varepsilon = V+Ir\)
 \(\varepsilon = I(R+r)\)









3.4 
Electrical Energy and Power 



Relationship between\(E\,,V\,,I\) and \(t\) 


\(E = V \,I\, t\) 








Relationship between\(P\,,V\) and \(I\)



\(P=V\,I\) 








Relationship between\(P\,,V\,,I\) and \(R\)



\(P=I^2\,R\)
\(P=\dfrac{V^2}{R}\)









Energy consumed for electrical devices, \(E\) 


\(E = P\,t\) 








Cost of consumption 


\(\text{Total cost} = E \times \text{Cost per kWh}\) 







