A series resonant circuit consists of a resistor of 10 Ω, a capacitor of 1 μF and an inductor of 1 mH. What is the value of the current flowing through this circuit at resonance if the applied voltage is 100 V AC?

Question

Question

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RRB ALP Mechanic Radio & TV 23 Jan 2019 Official Paper (Shift 3)

Answer 1

Concept:

Resonance:

In an electrical circuit, the condition that exists when the inductive reactance and the capacitive reactance are of equal magnitude, causing electrical energy to oscillate between the magnetic field of the inductor and the electric field of the capacitor, is termed resonance.
In a series RLC circuit at resonance, inductive reactance (XL) is equal to capacitive reactance (XC). The circuit becomes purely resistive, i.e. at resonance: XL = XC

The impedance at resonance becomes:

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} = R$

RRB JE EE 26 10Q FT0 Part1 D1

Calculation:

Current flowing through the circuit at resonance = $\frac{V}{Z}$

$= \frac{V}{R} = \frac{100}{10}$ =10 A