Question

A 80 KHz sinusoidal voltage has zero phase angle and a maximum amplitude of 20 mV. When this voltage is applied a cross the terminals of a capacitor, the resulting steady state current has a maximum amplitude of 0.7mA. What is the frequency of the current in radians per second?

Answer 1

The frequency of the current in a capacitor when subjected to an 80 KHz sinusoidal voltage is 160,000π radians per second, as the current and the voltage source have the same angular frequency.

Step-by-step explanation:

The student is asking about the frequency of the current in a capacitor when an 80 KHz sinusoidal voltage with a maximum amplitude of 20 mV is applied across its terminals. To calculate this frequency in radians per second (ω), we can use the relationship between angular frequency and frequency in hertz (f), which is ω = 2πf. The angular frequency will be the same for both voltage and the resulting current in a capacitive circuit, as they are driven by the same source. Therefore, the frequency of the current in radians per second is the same as the frequency of the voltage source, which would be ω = 2π × 80,000 Hz = 160,000π rad/s.