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Question

Find the value of the phase leg/lead between the current and voltage in the given series LCR circuit. Without making any other change, find the value of the additional capacitor, such that when 'suitably joined' to the capacitor ( C= 2μF) as shown, would make the power factor of this circuit unity.
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Solution

The current, I, leads the voltage, V, by an angle ϕ where

tanθ=XCXLR

Here, XL=1ωC=500Ω

and XL=ωL=100Ω, R=400Ω

tanϕ=1
ϕ=45o

The power factor becomes unity when ϕ=0o
Hence, we need to adjust C to a new value C'
where, XC=XL=100Ω

Thus the phase angle is 45o with the current leading the voltage.
To make power factor as unity, we need to have XC also equal to 100Ω . For this C needs to have a value of 10μF. We, therefore need to put an additional capacitor of i.e. 8μF in parallel with given capacitor.


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