An AC source operates at a maximum voltage of 60 V and is connected to a 0.7 mF capacitor. If the current across the capacitor is i(t) = i_MAX cos[(100 s⁻¹ )t], 
a) What is i_MAX? 
b) Draw the phasors for voltage across the capacitor and current in the circuit at t = 0.02 s. Assume that the current phasor begins at 0°.

• A. a) i_max = 4.2A b) θ_iC = 115^o θ_VC = 185^o
• B. a) i_max = 4.2A b) θ_iC = 185^o θ_VC = 115^o
• C. a) i_max = 4.2A b) θ_iC = 115^o θ_VC = 25^o
• D. a) i_max = 4.2A b) θ_iC = 25^o θ_VC = 115^o

Answer: (C)

Verified step by step guidance

1. Identify the given values: maximum voltage (Vmax) = 60 V, capacitance (C) = 0.7 mF, angular frequency (ω) = 100 s⁻¹.
2. Use the formula for capacitive reactance: Xc = 1 / (ωC). Substitute the given values to find Xc.
3. The maximum current (iMAX) can be found using Ohm's Law for AC circuits: iMAX = Vmax / Xc. Substitute the values of Vmax and Xc to find iMAX.
4. To draw the phasors, note that the current leads the voltage across a capacitor by 90 degrees. At t = 0.02 s, calculate the phase angle for the current using θiC = ωt.
5. For the voltage phasor, use the relationship θVC = θiC + 90°. Draw the phasors with the current phasor starting at 0° and the voltage phasor leading by 90°.