At what angular frequency is the voltage amplitude across (a)resistor, (b) inductor, (c) capacitor, in an LCR series circuit at maximum value?

Dear ravi

current in LC R circuit

i = V/[R² + (1/wC -wL)²]^1/2

 voltage across resistor  = iR  = VR /[R² + (1/wC -wL)²]^1/2

voltage across inductor  = iwL  = VwL /[R² + (1/wC -wL)²]^1/2

voltage across capacitor  = i/wc  = V /wC[R² + (1/wC -wL)²]^1/2

for maximum value differentiate each w.r.t w and put equal to zero

 for resister w=1/√LC

for inductor  =√[2C/(2L³ -CL²R²)]

for capacitor=√[(2L-CR²)/2L² ]

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