Electric

 

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  
     
 
 
3.2 Resistance
 
 
  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

 
     
 
  Non-ohmic 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 ohm-meter
  • 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  
  \(\text{Total cost} = E \times \text{Cost per kWh}\)