When an inductor \(L\) and a resistor \(R\) in series are connected across a \(12 \mathrm{~V}, 50…

When an inductor \(L\) and a resistor \(R\) in series are connected across a \(12 \mathrm{~V}, 50 \mathrm{~Hz}\) supply, a current of 0.5 A flows in the circuit. The current differs in the phase from applied voltage by \(\frac{\pi}{3}\) radian. Then the value of \(R\) is
  1. \(10 \Omega\)
  2. \(3 \Omega\)
  3. \(12 \Omega\)
  4. \(15 \Omega\)

Solution

Given situation following the figure below,
Given for AC circuit, \(V_{\mathrm{rms}}=12 \mathrm{~V} \text {, }\) frequency, \(f=50 \mathrm{~Hz}\), current, \(\quad I=0.5 \mathrm{~A}\), phase difference, \(\phi=\frac{\pi}{3}\) \(\therefore\) Impedance of the AC circuit, \(Z=\frac{V_{\text {rms }}}{I}=\frac{12}{0.5} \Rightarrow Z=24 \Omega\) Power factor, \(\Rightarrow \cos \phi=\frac{R}{Z} \Rightarrow \cos \frac{\pi}{3}=\frac{R}{24} \Rightarrow \frac{1}{2}=\frac{R}{24} \Rightarrow R=12 \Omega\)

Asked in: AP EAMCET 2019 (22 Apr Shift 1)

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