In this section, we will deal with an electric circuit, where an AC voltage is applied across a resistor. Before applying AC voltage across the resistor, let us know what an alternating current (AC) is. Electric current, which reverses its direction periodically and changes its magnitude continuously with time, is known as an alternating current.
AC Voltage Applied to a Resistor Derivation
Let us consider the circuit as shown below. We have a resistor and an AC voltage V, represented by the symbol ~, that produces a potential difference across its terminals that varies sinusoidally. Here, the potential difference or the AC voltage can be given as
Here, v_{m }is the amplitude of the oscillating potential difference and the angular frequency is given by ω.
As it works equally well for AC voltages and DC voltages. We saw that the voltage across the resistor and the current passing through it are both sinusoidal quantities and are represented by the graph shown in the figure above. Both the quantities are in phase with each other.
The instantaneous power in the circuit is given by,

Frequently Asked Questions – FAQs
What is direct current?
The unidirectional flow of electric charges is known as direct current.
Does AC change its magnitude continuously with time?
Yes, alternating current changes its magnitude continuously with time.
Define frequency of the electrical signal.
The number of cycles per second is known as frequency. Frequency is measured in hertz.
Stay tuned with BYJU’S to learn more about the AC voltages, the behaviour of the circuit when AC voltage is applied across a resistor and much more.