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A 200 Omega resistor is connected in ser...

A `200 Omega` resistor is connected in series with a `5(mu)F` capacitor. The voltage across the resistor is `V_(R )=(1.20 V) cos (2500 rad s^(-1))t`.
(a) Derive an expression for the circuit current.
(b) Determine the capacitive reactance of the capacitor.

Text Solution

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This is a series curcuit. The current is the same thrugh the capacitor as through the resistor. Our target variables are current I, capactive reactance `X_(C)` and capacitor voltage `V_(C)`.

(a) using `V_(R )-iR,` we find that current i in the resistor and through the circuit as a whole is
`i-(V_R)/(R )=((1.20 V)cos(2500 rad s^(-1))t)/(200 Omega)`
`=(6.0xx10^(-3)A) cos (2500 rad s^(-1))t`
(b) The capacitive reactance at `omega=2500 rad s^(-1)` is
`(X_C)=(1)/(omega C)=(1)/((2500 rad s^(-1)_(5.0xx10^(-6)F))=80 Omega`
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