MHT CET · Physics · Alternating Current
A resistance of \(200 \Omega\) and an inductor of \(\frac{1}{2 \pi} \mathrm{H}\) are connected in series to a.c. voltage of 40 V and 100 Hz frequency. The phase angle between the voltage and current is
- A \(\tan ^{-1}(1 / 5)\)
- B \(\tan ^{-1}(1 / 4)\)
- C \(\tan ^{-1}(1 / 3)\)
- D \(\tan ^{-1}(0 \cdot 5)\)
Answer & Solution
Correct Answer
(D) \(\tan ^{-1}(0 \cdot 5)\)
Step-by-step Solution
Detailed explanation
\( X_L = 2 \pi f L = 2 \pi (100 \, \mathrm{Hz}) \left( \frac{1}{2 \pi} \, \mathrm{H} \right) = 100 \, \Omega \) \( \phi = \tan^{-1} \left( \frac{X_L}{R} \right) = \tan^{-1} \left( \frac{100 \, \Omega}{200 \, \Omega} \right) = \tan^{-1}(0.5) \)
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