Question

In a series rlc circuit the rms voltage across the resistor and the inductor are respectively 400

Answer 1

The peak voltage across the capacitor is Eoc  = 400√2

Explanation:

Correct statement:

In series R–L–C circuit, the rms voltage across the resistor and inductor are respectively 400 V and 700 V.If the Equation for the applied voltage is E = 5002sin t, then the peak voltage across the capacitor is?

Solution:

E = 500√2 sin ωt

E(rms)  = Eo / √2 = 500√2/√2

             = 500 V

E(rms)^2  = E(R)^2 + ( EL - EC)^2

(500)^2 = (400)^2 + ( 700 - EC)^2

250000 = 160000 + ( 700 - EC)^2

250000 - 160000 = ( 700 - EC)^2

√90000  = ( 700 - EC)

300 - 700 =  - EC

-400  =  - EC

EC = 400

Peak voltage  "E(rmc)"  = Eoc/√2

Eoc  = 400√2

Hence the peak voltage across the capacitor is Eoc  = 400√2

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