I know power factor (cos $\phi$) =(Average power)/(rms power)=R/Z

But could not understand how to use it here ?

2 votes

Best answer

Powrer factor of circuit = 1

$R/Z= 1$ so $ R=Z $

$ Z= \sqrt {(wL-1/wC)^2 +R^2}$

but Z=R so,$

R^2=R^2 +(wL-1/wC)^2$

So $wL= 1/wC $

$1/wC= 40$

where $R $ would be resistance due to box only , as we don't see any other resistance

(provided the ammeter was ideal)

So for box,

Let $Z' $ be **reactance** of box.

So $ R/Z'= $

$ R/wL=3/5==> R/40 =cot\theta=3/4$

this gives R=30

Now R= Z for complete circuit,

so I= 3A ,

I think it would be 3A then .

The answer is given as D) 3A

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