In an \(A C\) circuit the potential differences across an inductance and resistance joined in series are respectively \(16 \mathrm{~V}\) and \(20 \mathrm{~V}\). The total potential difference of the source is

• A

  \(20.0 \mathrm{~V}\)
• Correct answer
  B

  \(25.6 \mathrm{~V}\)
• C

  \(31.9 \mathrm{~V}\)
• D

  \(53.5 \mathrm{~V}\)

Solution

\(V_L=16 \mathrm{~V}, V_R=20 \mathrm{~V}\). In the inductor the current lags by \(\frac{\pi}{2}\).
\(\begin{array}{ll} \therefore \quad V=\sqrt{V_L^2+V_R^2}=\sqrt{256+400} \\ \therefore \quad V_{\text {total }}=25.6 \mathrm{~V} . \end{array}\)

Hence, the correct answer is option: 'B'.