Question

A series resonant circuit has a resistance of 47 ohms, inductance of 2 H and capacitance of 2 μF with a supply voltage of 10 volts. The current through the circuit at resonance is:
1. 0.833 amp
2. 0.212 amp
3. 0.196 amp
4. 0 amp

Answer 1

Correct Answer - Option 2 : 0.212 amp

Concept:

We know that in a series RLC circuit impedance is given by

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

Current flowing in the circuit is given by \(I = \frac{V}{Z}\)

Where Z is impedance

R is resistance

XL is the inductive reactance

XC­ ­is capacitive reactance

At resonance condition, the inductive resistance is equal to capacitive reactance.

At this condition, Z = R which is the minimum value of impedance

At minimum impedance, the current flowing in the circuit is maximum

Calculation:

As, X_L = X_C

Net Impedance = R

Current \( = \frac{V}{R} = \frac{{10}}{{47}}\)

= 0.212 amp