Let's break down the problem step by step based on the given data:

Problem Setup:

• Capacitance: $C = 138 \, \mu\text{F} = 138 \times 10^{-6} \, \text{F}$
• Frequency: $f = 50 \, \text{Hz}$
• Peak Voltage: $V_{\text{peak}} = 8 \, \text{V}$

The angular frequency ($\omega$) is related to the frequency: $\omega = 2 \pi f = 2 \pi (50) = 100 \pi \, \text{rad/s}.$

The capacitive reactance ($X_C$) is given by: $X_C = \frac{1}{\omega C}.$

1. Find Peak Current ($I_{\text{peak}}$): The peak current is given by Ohm's law for AC circuits: [ I_{\text{peak}} = \frac{