The alternating current in a circuit is described by the graph shown in the figure. Calculate the root mean square $(I_{rms})$ current for this waveform.

(N/A) The given waveform is a periodic square wave. The current $I(t)$ takes the value $I_1 = 1 \text{ A}$ for time interval $0 < t < T/2$ and $I_2 = -2 \text{ A}$ for time interval $T/2 < t < T$.
The root mean square current $I_{rms}$ is defined as:
$I_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} I^2(t) dt}$
Substituting the values:
$I_{rms} = \sqrt{\frac{1}{T} \left[ \int_{0}^{T/2} (1)^2 dt + \int_{T/2}^{T} (-2)^2 dt \right]}$
$I_{rms} = \sqrt{\frac{1}{T} \left[ (1 \times T/2) + (4 \times T/2) \right]}$
$I_{rms} = \sqrt{\frac{1}{T} \left[ \frac{T}{2} + 2T \right]} = \sqrt{\frac{1}{T} \left( \frac{5T}{2} \right)}$
$I_{rms} = \sqrt{2.5} \approx 1.58 \text{ A}$.