AC voltage applied to a resistor is a voltage that varies sinusoidally with time, causing the current through the resistor to also vary sinusoidally. This means both the voltage and current alternate direction periodically.
Understanding AC Voltage and Resistors
When an Alternating Current (AC) voltage source is connected to a resistor, the voltage across the resistor changes polarity and magnitude over time. This is in contrast to Direct Current (DC) voltage, which provides a constant voltage level. The most common form of AC voltage is sinusoidal, which can be mathematically represented as:
- *V(t) = Vpeak sin(ωt + φ)**
Where:
- V(t) is the instantaneous voltage at time t.
- Vpeak is the peak voltage (the maximum voltage value).
- ω is the angular frequency (ω = 2πf, where f is the frequency in Hertz).
- t is time.
- φ is the phase angle in radians.
How a Resistor Behaves with AC Voltage
A resistor opposes the flow of current. According to Ohm's Law, the relationship between voltage (V), current (I), and resistance (R) is:
- V = IR
When AC voltage is applied, the current through the resistor also varies sinusoidally, in phase with the voltage (for a purely resistive circuit). Therefore, the current can be described as:
- *I(t) = Ipeak sin(ωt + φ)**
Where:
- I(t) is the instantaneous current at time t.
- Ipeak is the peak current (Ipeak = Vpeak / R).
Key Characteristics
- Frequency: The frequency of the AC voltage (and current) determines how many times the voltage changes polarity per second. Common frequencies are 60 Hz (in North America) and 50 Hz (in Europe).
- RMS Voltage: The Root Mean Square (RMS) voltage is a way to represent the "effective" voltage of an AC signal. It's the equivalent DC voltage that would produce the same amount of power dissipation in a resistor. VRMS = Vpeak / √2.
- Power Dissipation: The instantaneous power dissipated by the resistor is given by P(t) = V(t) I(t). The average power dissipated is Pavg = VRMS2 / R = IRMS2 R.
Example
Imagine a 120V (RMS), 60Hz AC voltage applied to a 100 Ohm resistor.
- Peak Voltage: Vpeak = VRMS √2 = 120V √2 ≈ 169.7 V
- Peak Current: Ipeak = Vpeak / R = 169.7 V / 100 Ohm ≈ 1.697 A
- RMS Current: IRMS = VRMS / R = 120 V / 100 Ohm = 1.2 A
- Average Power Dissipation: Pavg = VRMS2 / R = (120 V)2 / 100 Ohm = 144 W
In summary, AC voltage applied to a resistor results in a continuously changing voltage and current across the resistor, leading to power dissipation. The voltage and current are sinusoidal and in phase, with magnitudes determined by Ohm's Law and the resistance value.
