Explain AC voltage applied to a resistor and explain it with necessary graph.

Explanation

Figure shows a resistor connected to an ac voltage.

Here consider a source which produces sinusoidally varying potential difference across its terminals. Such type of potential difference is called ac voltage.
`:.` ac voltage `V = V_(m) sin omega t ` .....(1)
where `V_(m)` is the amplitude of the oscillating potential difference. Means maximum voltage and `omega` is its angular frequency.
From equation (1), V = IR
where I can be found by applying Kirchhoff.s loop rule,
`:.` IR = `V_(m) sin omegat `
`:. I = ( V_(m))/( R ) sin omega t `
but `( V_(m))/( R ) = I_(m)`
`:.` I `= I_(m) sin omega t ` .....(2)
where the current amplitude is,
`I_(m) = ( V_(m))/( R ) ` is just a Ohm.s law.
This relation works equally for both ac and dc voltage or current (signal ).
The voltage across a pure resistor and current through it are plotted as a function of time is shown in below graph.

In a pure resistor, the voltage and current are in phase.
The minima, zero and maxima occur at the same respective times.
The voltage and current are in phase with each other in pure resistor. Both reach zero. minimum and maximum values at the same time.
Here both V and I reach zero, minimum and maximum values at the same time, so the voltage and current are in phase with each other.