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Physics Question on Dimensional Analysis

An inductor of 0.5 mH, a capacitor of 200 μF and a resistor of 2 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ × 102 Hz

Answer

The correct answer is 5
ωL=1ωCωL = \frac{1}{ωC}
⇒ω=1LC=15×10−4×2×10−4⇒ ω = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{5 × 10^{-4} × 2 × 10^{-4}}}
⇒ω=10410rad/s⇒ ω = \frac{104}{\sqrt{10}} rad/s
⇒ƒ=12π×10410Hz⇒ ƒ = \frac{1}{2π} × \frac{104}{\sqrt{10}} Hz
⇒ƒ≃500Hz⇒ ƒ ≃ 500 Hz
Therefore , the frequency of ac source will be 5 × 102 Hz