Alternating Currents

Alternating Currents

Alternating current (A.C) periodically varies from positive to negative current. If the alternating current supply is plotted against time, a sinusoidal graph is formed showing that the electrons in the wire move back and forth in simple harmonic motion (SHM). The same concept could be used for plotting voltage against time.

Root-Mean-Square Current

Root-Mean-Square (rms) is used to compare AC and DC (Direct Current) currents. The rms for direct current or voltage represents the value of direct current or voltage that will produce the same power dissipation as alternating current. The rms value is calculated by the square root of the mean of the squares of all values of voltage in one full cycle.

To calculate the rms current \left(I_{rms}\right), the following equation can be used:

I_{rms} = \dfrac{I_0}{\sqrt{2}}

where I_{rms} is the rms current and I_0 is the peak current. Both are measured in amps \left(\text{A}\right).

To calculate the rms voltage \left(V_{rms}\right), the following equation can be used:

V_{rms} = \dfrac{V_0}{\sqrt{2}}

where V_{rms} is the rms voltage and V_0 is the peak voltage. Both are measured in volts \left(\text{V}\right).

Example: The peak current read from an oscilloscope trace is 2.5 \: \text{A}. What is the rms current?

[1 mark]

I_{rms} = \dfrac{I_0}{\sqrt{2}}

I_{rms} = \dfrac{2.5}{\sqrt{2}}

I_{rms} = 1.8 \: \text{A}