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# 18. 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
*N*_{p} turns and voltage *V*_{p} and secondary coil of *N*_{s} turns and voltage *V*_{s} 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.

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