• Electromotive force is the energy converted into electrical energy when 1 C of charge passes through the power source

P.D. and E.M.F.

Internal Resistance

• Internal resistance is the resistance to current flow within the power source; it reduced p.d. when delivering current
  
• V = Ir – E
• Voltage across the resistor: V = IR
• Voltage lost to internal resistance: V = Ir
• Thus e.m.f.: E  = IR + Ir
  • E = I(R + r)

Kirchhoff’s First Law

• Sum of currents into a junction is equal to the sum of currents out of the junction
• Kirchhoff’s first law is another statement of the law of conservation of charge

Kirchhoff’s Second Law

• Sum of e.m.fs in a closed circuit is equal to the sum of the potential differences
• Kirchhoff’s second law is another statement of the law of conservation of energy

Applying Kirchhoff’s Laws

1. Calculate the current in each of the resistors
   
   • Using Kirchhoff’s first law:
     • I₃ = I₁ + I₂
   • Using Kirchhoff’s second law on loop ABEF:
     • 3 = 30I₃ + 10I₁
   • Using Kirchhoff’s second law on loop CBED:
     • 2 = 30I₃
   • Using Kirchhoff’s second on loop ACDF:
     • 3 – 2 = 10I₁
   • Solve the simultaneous equations:
     • I₁ = 0.1
     • I₂ = -0.033
     • I₃ = 0.067

Deriving Effective Resistance in Series

• From Kirchhoff’s second law:
  • E = ∑IR
  • IR = IR₁ + IR₂
• Current is constant, therefore:
  • R = R₁ + R₂

Deriving Effective Resistance in Parallel

• From Kirchhoff’s first law:
  • I = ∑I
  • I = I₁ + I₂
  • ^V/_R = ^V/_R1 + ^V/_R2
• Voltage is constant, therefore;
  • ¹/_R = ¹/_R1 + ¹/_R2

Properties of Magnets

• A potential divider divides the voltage into smaller parts
  
  • ^V_out/_Vin = ^R₂/_RTotal
• Usage of a thermistor at R₁:
  • Resistance decreases with increasing temperature
  • It can be used in potential divider circuits to monitor and control temperatures
• Usage of an LDR at R₁:
  • Resistance decreases with increasing light intensity
  • It can be used in potential divider circuits to monitor light intensity

Potentiometers

• A potentiometer is a continuously variable potential divider used to compare potential differences
• Potential difference along the wire is proportional to the length of the wire
• It can be used to determine the unknown e.m.f. of a cell
• This can be done by moving the sliding contact along the wire until it finds the null point that the galvanometer shows a zero reading; the potentiometer is balanced
• For example:
  1. E₁ is 10 V, distance XY is equal to 1 m. The potentiometer is balanced at point T which is 0.4 m from X. Calculate E₂
     
     • • ^E₁/_E2 = ^L₁/_L2
       • ¹⁰/_E2 = ¹/_0.4
       • E₂ = 4 V