Voltage - Physics 152 (or Phys 2) question

Question

In a series circuit, a generator (1400 Hz, 14.0V) is connected to a 12.0-Ω resistor, a 3.90-µF capacitor, and a 5.90-mH inductor. Find the voltages across (a) the resistor, (b) the capacitor, and (c) the inductor. Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

Answer 1

Some formulas we need to use;

X(C) = 1 / (2 * π * f * C)

Calculate the impedance of the inductor:

X(L) = 2 * π * f * L

(a) Voltage across the resistor: V_R = I_RMS * R

(b) Voltage across the capacitor: V_C = I_RMS * X_C

(c) Voltage across the inductor: V_L = I_RMS * X_L

X(C) = 1 / (2 * 3.14 * 1400 * 3.9 * 10^-6C) = 29.1

X(L) = 2 * 3.14 * 1400 * 5.9 * 10^-3 = 51.9

X(R) = 12

Z = √(R² + (X_L-X_C)²) = 25.77 Ω

I = V/Z = 14/25.77 = 0.54A.

I(t) = 0.54sin(8792t)

Power, use P = I²R for each element