Final answer:
To find the rms current in an RCL circuit, we need to calculate the impedance at the given frequencies and use Ohm's Law to find the current. The impedance can be found using the formula Z = sqrt(R^2 + (X_L - X_C)^2), where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance.
Step-by-step explanation:
The impedance of an RCL circuit can be found using the formula Z = sqrt(R^2 + (X_L - X_C)^2), where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance. At a frequency of 500 Hz, the inductive reactance is given by X_L = 2πfL, and the capacitive reactance is given by X_C = 1/(2πfC). We can substitute these values into the impedance formula to find the impedance at 500 Hz. The same process can be used to find the impedance at 7.50 kHz.
To calculate the rms current, we can use Ohm's Law, which states that I = V / Z, where I is the current, V is the voltage, and Z is the impedance of the circuit. We can substitute the given values into this equation to find the rms current at each frequency.
The question is asking to determine the rms current in an RLC circuit that contains a 148 Ω (ohms) resistor, a 1.50 μF (microfarads) capacitor, and a 35.7 mH (millihenrys) inductor with a generator frequency of 512 Hz and an rms voltage of 35.0 V.
To calculate this, we need to find the circuit's impedance first, and then apply Ohm's Law.
The impedance (Z) of an RLC circuit is given by:
Z = √( R2 + (XL - XC)2 ), where XL = 2πfL is the inductive reactance, and XC = 1 / (2πfC) is the capacitive reactance.
The rms current (Irms) can then be calculated using the formula:
Irms = Vrms / Z where Vrms is the rms voltage of the source.
The rms current can then be calculated using Ohm's Law, which states that I = V / Z, where I is the current, V is the voltage, and Z is the impedance of the circuit.