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?

Question

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?

Philoid · Accepted Answer

Given:
Power of an electrical device: P = 2kW
voltage: V = √50000 V
RMS value of voltage : V_RMS = 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 X_C>X_L

Here, R is the resistance of the circuit, X_L is the inductive reactance and X_C is the Capacitive reactance.

Also,

Substituting we get,

(ii)
Substituting value of R we get,

(iii)
I_M = I_o. Here I_o is the output current.
RMS value of current is

Also,

Now, if values of R, X_C and X_L 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, X_C and X_L would make the power half times the present one.