An alternating voltage given by V= 70 sin 100 pi t is connected across a pure resistor of 25 ohm. Find

1.     the frequency of the source
2. the rms current through the resistor.

Dear Student,

Please find below the solution to the asked query:

Given Alternating Voltage equation is,

$$\begin{gathered} V=70 \sin 100\pi t \\ So, \\ \omega =100 \pi \Rightarrow f=\frac{\omega }{2\pi }=\frac{100 \pi }{2 \pi } \\ \Rightarrow f=50 Hz \end{gathered}$$

The rms current is.

$$\begin{gathered} I_{rms}=\frac{V_{rms}}{R}=\frac{{\displaystyle \raisebox{1ex}{$V_0$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}$}\right.}}{R}=\frac{70}{25\times \sqrt{2}}=\frac{14}{5\sqrt{2}}=\frac{14}{7.07} \\ \Rightarrow I_{rms}=1.98 A \end{gathered}$$

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