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A $44 \mathrm{mH}$ inductor is connected to $220 \mathrm{~V}, 50 \mathrm{~Hz}$ ac supply. Determine the rms value of the current in the circuit.
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Verified Answer
Given: inductance $\mathrm{L}=44 \mathrm{mH}$
voltage $\mathrm{E}_{\mathrm{v}}=220 \mathrm{~V} \quad$ frequency $v=50 \mathrm{~Hz}$
To find: rms current
Formula: $I_v=\frac{E_v}{X_L} \quad I_v=\frac{E_v}{X_L}=\frac{E_v}{2 \pi v L}$
$$
\begin{aligned}
\Rightarrow \mathrm{I}_{\mathrm{v}} &=\frac{220}{2 \times 3.14 \times 50 \times 44 \times 10^{-3}} \\
&=\frac{10}{100 \times 2 \times 3.14 \times 10^{-3}} \\
&=\frac{100}{6.28}=15.9 \mathrm{~A}
\end{aligned}
$$
voltage $\mathrm{E}_{\mathrm{v}}=220 \mathrm{~V} \quad$ frequency $v=50 \mathrm{~Hz}$
To find: rms current
Formula: $I_v=\frac{E_v}{X_L} \quad I_v=\frac{E_v}{X_L}=\frac{E_v}{2 \pi v L}$
$$
\begin{aligned}
\Rightarrow \mathrm{I}_{\mathrm{v}} &=\frac{220}{2 \times 3.14 \times 50 \times 44 \times 10^{-3}} \\
&=\frac{10}{100 \times 2 \times 3.14 \times 10^{-3}} \\
&=\frac{100}{6.28}=15.9 \mathrm{~A}
\end{aligned}
$$
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