17. Alternating Currents

17. Alternating Currents

  • The root-mean-square value of an alternating current is equivalent to the steady direct current that would dissipate heat at the same rate as the alternating current in a given resistor.
  • For a sinusoidal source,
    (a) the root mean square value of the current is given by I_{rms}=\frac{I_o}{\sqrt{2}}.
    (b) the mean or average power < P > absorbed by a resistive load is half the maximum power.
    <P>=\frac{1}{2}P_o=\frac{1}{2}{I_o}{V_o}=\frac{1}{2}{I_o}^2R =\frac{V_o^2}{2R}.
  • An a.c. transformer is a device for increasing or decreasing an a.c. voltage. It consists of a primary coil of Np turns and voltage Vp and secondary coil of Ns turns and voltage Vs wrapped around an iron core.
  • For an ideal transformer (assuming no energy is lost), the following equation is obeyed
    \frac{N_s}{N_p}=\frac{V_s}{V_p}=\frac{I_p}{I_s}.
  • Power loss in the transmission lines is minimized if the power is transmitted at high voltages (i.e. low currents) since P_{loss}=I^2R where I is the current through the cables and R is the resistance of the cables.
  • The equation P=\frac{V^2}{R} is often mistakenly used to suggest that power lost is high when voltage of transmission is high. In fact, V refers to the potential difference across the cables, which often have but a fraction of the overall resistance through which the current passes.