Final answer:
To find the voltage dropped across the resistor, inductor, and capacitor in an AC circuit with a frequency of 400 Hz and components connected in series, we can use the formulas for inductive reactance and capacitive reactance.
Step-by-step explanation:
In an AC circuit with a frequency of 400 Hz, a 167-ohm resistor, a 0.0119 H inductor, and a 16.6 μF capacitor are connected in series. To determine the voltage dropped across each component, we can use the formulas for inductive reactance (XL) and capacitive reactance (XC).
1. The voltage dropped across the resistor can be calculated using Ohm's Law: Vresistor = I * R, where I is the current flowing through the circuit and R is the resistance. In this case, the current can be calculated using the formula I = V / Z, where V is the voltage amplitude and Z is the impedance of the circuit. The impedance can be calculated using the formula Z = sqrt(R^2 + (XL - XC)^2). Once the current is determined, the voltage dropped across the resistor can be calculated.
2. The voltage dropped across the inductor can be calculated using the formula VL = I * XL, where XL is the inductive reactance. The inductive reactance can be calculated using the formula XL = 2 * π * f * L, where f is the frequency and L is the inductance.
3. The voltage dropped across the capacitor can be calculated using the formula VC = I * XC, where XC is the capacitive reactance. The capacitive reactance can be calculated using the formula XC = 1 / (2 * π * f * C), where C is the capacitance.