In a series circuit, a generator (1400 Hz, 12.0 V) is connected to a 15.0- resistor, a 3.80-μF capacitor, and a 5.70-mH inductor. Find the voltages across (a) the resistor, (b) the capacitor, and (c) the inductor.

To find the voltages across the resistor, capacitor, and inductor in a series circuit, you can use the formulas for impedance and voltage in different electrical components.

1. Calculate the impedance of the resistor using Ohm's Law:
Impedance (Z_resistor) = Resistance (R_resistor) = 15.0 Ω

2. Calculate the impedance of the capacitor using the formula:
Capacitive Reactance (Xc) = 1 / (2πfC), where f is the frequency and C is the capacitance.
Xc = 1 / (2π(1400 Hz)(3.80 × 10^-6 F))
Impedance (Z_capacitor) = Xc

3. Calculate the impedance of the inductor using the formula:
Inductive Reactance (Xl) = 2πfL, where f is the frequency and L is the inductance.
Xl = 2π(1400 Hz)(5.70 × 10^-3 H)
Impedance (Z_inductor) = Xl

4. Use the formula for the total impedance (Z_total) in a series circuit:
Z_total = Z_resistor + Z_capacitor + Z_inductor

5. Calculate the total current (I) using Ohm's Law:
I = V_generator / Z_total, where V_generator is the voltage of the generator (12.0 V).

6. Calculate the voltage across each component using Ohm's Law:
Voltage across Resistor (V_resistor) = I × Z_resistor
Voltage across Capacitor (V_capacitor) = I × Z_capacitor
Voltage across Inductor (V_inductor) = I × Z_inductor

Substituting the calculated values into the above formulas will give you the desired voltages:

(a) V_resistor = I × Z_resistor
(b) V_capacitor = I × Z_capacitor
(c) V_inductor = I × Z_inductor