JEE Mains · Physics · STD 12 -7. Alternating current
An inductor of \(10\) mH, capacitor of \(0.1\ \mu\)F and a resistor of \(100\ \Omega\) are connected in series across an \(a.c\) power supply \(220\) V, \(70\) Hz. The power factor of the given circuit is \(0.5\). The difference in the inductive reactance and capacitance reactance is \(\sqrt{3}\alpha\ \Omega\). The value of \(\alpha\) is _____.
- A 50
- B 100
- C 125
- D 150
Answer & Solution
Correct Answer
(B) 100
Step-by-step Solution
Detailed explanation
The power factor of an LCR series circuit is given by \(\cos \phi = \dfrac{R}{Z}\). Given \(\cos \phi = 0.5\) and \(R = 100 \ \Omega\). Substituting the values, we get: \(0.5 = \dfrac{100}{Z} \Rightarrow Z = 200 \ \Omega\) The impedance \(Z\) of the circuit is also given by:…
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