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An electrical device draws 2 kW power fr...

An electrical device draws 2 kW power from ac mains voltage 223 `V_(rms)`. The current differs (lags) in phase by `phi=tan^(-1)(-(3)/(4))` as compared to voltage. The resistance R in the circuit is

A

`15 Omega`

B

`20 Omega`

C

`25 Omega`

D

`30 Omega`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `P= 2k W = 2xx10^(3)W`
`V_("rms")=223 V, tan phi = -(3)/(4)`
As, `P=(V_("rms")^(2))/(Z)`
`rArr Z=(V_("rms")^(2))/(Z)=((223)^(2))/(2000)=(49729)/(2000)=24.86 Omega` or `Z ~~ 25 Omega`
`tan phi = (X_(C )-X_(L))/(R )=-(3)/(4) therefore X_(C )-X_(L)=-(3)/(4) R`.
`therefore (25)^(2)=R^(2)+(-(3)/(4)R)^(2)`
`625 = R^(2)+(9)/(16)R^(2)=(25 R^(2))/(16)`
`R^(2)=(625xx16)/(25)=400 rArr R=20 Omega`
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