Question

For the RLC circuit shown below, the root mean square current \( I_{{rms}} \) at the resonance frequency is _______amperes. (rounded off to the nearest integer)

\[ V_{{rms}} = 240 \, {V}, \quad R = 60 \, \Omega, \quad L = 10 \, {mH}, \quad C = 8 \, \mu {F} \]

Hint:

At resonance in a series RLC circuit, the current is determined by the total resistance \( R \), and the reactances of the inductor and capacitor cancel each other out.

Answer 1

Correct Answer: 4

In a series RLC circuit at resonance, the impedance \( Z_{{resonance}} \) is equal to \( R \), the resistance of the resistor, because the inductive reactance and capacitive reactance cancel each other out. The formula for the root mean square current \( I_{{rms}} \) at resonance is given by: \[ I_{{rms}} = \frac{V_{{rms}}}{R} \] Where:
\( V_{{rms}} \) is the root mean square voltage across the circuit,
\( R \) is the resistance of the resistor.
Substituting the given values: \[ I_{{rms}} = \frac{240}{60} = 4 \, {A} \] Thus, the root mean square current at the resonance frequency is: \[ I_{{rms}} = 4 \, {A} \]