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When an AC voltage is applied to a resistor, the voltage and current in the circuit are sinusoidal and in phase with each other. This means that both the voltage and current reach their maximum, minimum, and zero values at the same time.

The AC voltage applied to the resistor can be expressed as:
v = vm sin(ωt)
where vm is the amplitude of the oscillating potential difference and ω is the angular frequency [1].

Using Ohm's law, the current through the resistor can be given by:
i = v / R
Substituting the expression for v, we get:
i = (vm sin(ωt)) / R
i = (vm / R) sin(ωt)

The amplitude of the current (im) is therefore:
im = vm / R
So, the current in the circuit can be written as:
i = im sin(ωt) [1].

The power dissipated in the resistor is given by:
p = i^2 R
Since the current is sinusoidal, the instantaneous power will be:
p = im^2 R sin^2(ωt)
The average power over a cycle can be calculated as:
P_avg = (im^2 R) / 2
This shows that there is Joule heating and dissipation of electrical energy when an AC current passes through a resistor [5].

In summary:

• The voltage and current are in phase.
• The current varies sinusoidally with time.
• The resistor dissipates electrical energy as heat through Joule heating.

References: [1]leph107.pdf, page 2 [5] leph107.pdf, page 3

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What happens when you apply AC voltage to a resistor?