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In the circuit shown in the figure, find...

In the circuit shown in the figure, find:
(a) the reactance of the circuit
(b) impedance of the circuit
(c )the current
(d) readings of the ideal AC voltmeters(these are hot wire instruments and read rms values)

Text Solution

Verified by Experts

`(a)X_(L)=2pifL=2pixx50xx(2)/(pi)=200Omega`
`X_(C)=(1)/(2pi50(100)/(pi)xx10^(-6))=100Omega`
`therefore` The reactance of the circuit `X=X_(L)-X_(C)=200-100=100Omega`
Since, `X_(L)-X_(C)` the circuit is called inductive.
(b) impedence of the circuit `Z=sqrt(R^(2)+X^(2))=sqrt(100^(2)+100^(2))=100Omega`
(c ) the current `I_("rms")=(V_("rms"))/(Z)=(200)/(100sqrt2)=sqrt2A`
(d) readings of the ideal voltmeter
`V_(1)=I_("rms")X_(L)=200sqrt2"Volt"`
`V_(2)=I_("rms")R=100sqrt2"Volt"`
`V_(3)=I_("rms")X_(c)=100sqrt2"Volt"`
`V_(4)=I_("rms")sqrt(R^(2)+X_(L)^(2))=100sqrt10"Volt"`
`V_(5)=I_("rms")Z=200"volt"` which also happens to be the voltage of source.
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