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Figure shows a series LCR circuit connec...

Figure shows a series LCR circuit connected to a variable frequency 230 V source. `L = 5.0 H, C = 80 mu F, R = 40 Omega`.

Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.

Text Solution

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Given, the rms value of voltage `V_("ims")=230 V`
Inductance L = 5H
Capacitance `C = 80 mu f = 80xx10^(-6)F`
Resistance `R = 40 Omega`
The rms potential drop across L
`V_(L)=I_("rms")X_(L)`
`= I_("rms")omega_(r )L=5.75xx50xx5=1437.5V`
The rms potential drop across R
`V_(R )=I_("rms")R=5.75xx40=230 V`
The rms potential drop across C,
`V_(C )=I_("rms")xx X_(C )=I_("rms")xx(1)/(omega_(r )C)`
`= 5.75xx(1)/(50xx80xx0^(-6))`
`= 1437.5 V`
Potential drop across LC combinations
`= I_("rms")(X_(L)-X_(C ))`
`= I_("rms")(X_(L)-X_(L))=0(because X_(L)-X_(C ))`
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