Alternating Current

Step 1: Understanding alternating current.
Alternating current (AC) varies in magnitude and direction with time, typically in a sinusoidal pattern. The current flows first in one direction and then in the opposite direction, with the cycle repeating periodically.
Step 2: The average value of alternating current.
The average value of alternating current over a complete cycle is zero. This is because the positive and negative half-cycles of AC cancel each other out when averaged over a full cycle.
Step 3: Conclusion.
The average value of alternating current over a complete cycle is zero.

Step 1: Find the frequency of the source.
The given equation for voltage is , which is of the form: where is the amplitude and is the angular frequency. The angular frequency is related to the frequency by: Substitute : Solving for :
Step 2: Find the r.m.s current through the resistor.
The r.m.s. current in a resistor is given by: where is the resistance and is the amplitude of the voltage. Substituting the values:

Step 1: r.m.s. value of current.
The r.m.s. value of current is given by the formula: where is the supply voltage and is the resistance. Substituting the given values:
Step 2: Net power consumed.
The net power consumed by the resistor is given by: Substituting the value of and :
Step 3: Conclusion.
The r.m.s. value of current is , and the net power consumed is .