Determine the rms voltage drop across the capacitor in the circuit.
A) 55 V
B) 77 V
C) 110 V
D) 154 V
E) 198 V

Question

Determine the rms voltage drop across the capacitor in the circuit. 
A) 55 V 
B) 77 V 
C) 110 V 
D) 154 V 
E) 198 V

Quizplus · Accepted Answer

To find the rms voltage drop across the capacitor, we can use the formula:

V_rms = V_peak / sqrt(2)

In this circuit, the capacitor is in parallel with the 220 V AC source, so the voltage across the capacitor is also 220 V. However, the capacitor acts as a voltage divider with the 330 ohm resistor, so the voltage across the capacitor is:

V_cap = V_source x (R2 / (R1 + R2))
      = 220 V x (330 ohm / (330 ohm + 1000 ohm))
      = 66 V

Using the formula above, we can find the rms voltage:

V_rms = 66 V / sqrt(2)
      = 46.7 V

However, we also need to take into account the phase angle between the voltage across the capacitor and the current through the circuit. Since this is a purely capacitive circuit, the current leads the voltage by 90 degrees. This means that the true rms voltage drop across the capacitor is:

V_rms = V_cap / sqrt(2) x cos(90 degrees)
      = V_cap / sqrt(2) x 0
      = 0 V

Since the capacitor only blocks the DC component of the input voltage, the true rms voltage across the capacitor is simply the AC component of the input voltage, which is 110 V. Therefore, the answer is:

Answer: C) 110 V

Determine the Rms Voltage Drop Across the Capacitor in the Circuit