What is the total impedance (in Ohms) of the series RLC circuit containing resistance of 8 Ohms, capacitive reactance of 2 Ohms and inductive reactance of 8 Ohms connected in series across a 100 V, 50 Hz supply?

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This question was previously asked in

SSC JE EE Previous Year Paper 12 (Held On: 27 Jan 2018 Evening)

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Answer 1

Concept:

In a series RLC circuit, the impedance is given by

\(Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}}\)

R is resistance

XL is inductive reactance = ωL

XC is capacitive reactance = -1/ωC

(XL – XC) is net reactance

At the resonant frequency, inductive reactance is equal to capacitive reactance i.e. XL = XC

So, at this condition the impedance is minimum, and it is equivalent to R.

Explanation:

Given that, resistance (R) = 8 Ω

Capacitive reactance (X_C) = 2 Ω

Inductive reactance (X_L) = 8 Ω

Net Impedance Z is calculated as:

\(Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} \)

\(Z= \sqrt {{8^2} + {{\left( {8 - 2} \right)}^2}} = 10\;{\rm{\Omega }}\)