A resistor of `200 Omega` and a capacitor of `1.50 mu F` are connected in series to a 220V, 50 Hz ac source. Calculate the voltage (rms) across the re

Question

A resistor of `200 Omega` and a capacitor of `1.50 mu F` are connected in series to a 220V, 50 Hz ac source. Calculate the voltage (rms) across the re

A resistor of `200 Omega` and a capacitor of `1.50 mu F` are connected in series to a 220V, 50 Hz ac source.
Calculate the voltage (rms) across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage ? If yes, resolve the paradox.

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Given
`R = 200 Omega. C = 15.0 mu F = 15.0 xx 10^(-6)F`
`V = 220V, v = 50 Hz`
In order to calculate the current, we need the impedance of the circuit. It is
`Z = sqrt(R^(2)+X_(C )^(2))=sqrt(R^(2)+(2pi vC)^(-2))`
`= sqrt((200Omega)^(2)+(2xx3.14xx50xx10^(-6)F)^(-2))`
`= sqrt((200Omega)^(2)+(212Omega)^(2))=291.5Omega`
Therefore, the current in the circuit is
`I =(V)/(Z)=(220V)/(291.5 Omega)=0.755 A`