Question 21.1: What Is the rms Current? GOAL Perform basic AC circuit calcu...

Obtain the maximum voltage by comparison of the given expression for the output with the general expression:

\Delta v=(2.00\times10^{2}\,\mathrm{V})\,\sin\,2\pi \mathrm{ft}\qquad\Delta v=\Delta V_{\mathrm{max}}\sin\,2\pi\mathrm{ft}

→  \Delta V_{\mathrm{max}}=2.00\times10^{2}\,\mathrm{V}

Next, substitute into Equation 21.3 to find the rms voltage of the source:

\Delta V_{\mathrm{rms}}={\frac{\Delta V_{\mathrm{max}}}{\sqrt{2}}}={\frac{{2}.00\ \times{10^{2}\,\mathrm{V}}}{\sqrt{2}}}=\ {141\,{\mathrm{V}}}

\Delta V_{\mathrm{rms}}={\frac{\Delta V_{\mathrm{max}}}{\sqrt{2}}}=0.707  \Delta V_{max}         [21.3]

Substitute this result into Ohm’s law to find the rms current:

I_{\mathrm{rms}}={\frac{\Delta V_{\mathrm{rms}}}{R}}={\frac{141\,\mathrm{V}}{1.00~\times~10^{2}\,\Omega}}=\ \ {1.41\,\mathrm{A}}

REMARKS Notice how the concept of rms values allows the handling of an AC circuit quantitatively in much the same way as a DC circuit.