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DC Circuits

  • 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

    • Vout/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
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