An electrical device draws 2kW power from AC mains The current differs (lags) in phase by as compared to voltage. Find (i) R, (ii) XC – XL, and (iii) IM. Another device has twice the values for R, XC and XL. How are the answers affected?


Given:
Power of an electrical device: P = 2kW
voltage: V = √50000 V
RMS value of voltage : VRMS = 223 V
tanϕ = -3/4
Formula used:
(i)
Power is given as

Here, P is the power, V is the voltage,I is the current and Z is the impedance.
Also, V2 = 50000 V



We know that as XC>XL

Here, R is the resistance of the circuit, XL is the inductive reactance and XC is the Capacitive reactance.



Also,




Substituting we get,




(ii)
Substituting value of R we get,


(iii)
IM = Io. Here Io is the output current.
RMS value of current is



Also,



Now, if values of R, XC and XL are doubled.
Then value of tanϕ would remain same. Value of Z will be doubled. As power and impedance have inverse relation. Power would become half .
Hence, doubling the values of R, XC and XL would make the power half times the present one.


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