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)
\[ V_{{rms}} = 240 \, {V}, \quad R = 60 \, \Omega, \quad L = 10 \, {mH}, \quad C = 8 \, \mu {F} \]
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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.
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:
\[
I_{{rms}} = 4 \, {A}
\]
