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Question
In a series LCR circuit, obtain the condition under which watt-less current flows in the circuit ?
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Solution
Average power dissipated through a series LCR circuit is given by \[P_{av} = E_v I_v \cos\left( \phi \right)\]
where, Ev = rms value of alternating voltage
Iv = rms value of alternating current
Φ = phase difference between current and voltage
For wattless current, the power dissipated through the circuit should be zero.
\[i . e . , \cos\left( \phi \right) = 0\]
\[ \Rightarrow \phi = \frac{\pi}{2}\]
Hence, the condition for wattless current is that the phase difference between the current and voltage should be π/2 and the circuit is purely inductive or purely capacitive.
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