A.C. (alternating current) fundamentals are an important aspect of electrical engineering, particularly in understanding how electrical circuits behave when the current and voltage alternate sinusoidally over time. A purely resistive circuit is one of the simplest types of circuits and consists only of resistive elements, such as resistors, without any reactive elements like capacitors or inductors. Let's delve into the key concepts related to purely resistive AC circuits.
Ohm's Law: Ohm's law still holds in AC circuits for resistive elements, just as it does in DC circuits. The relationship between voltage (V), current (I), and resistance (R) is given by V = I * R.
Impedance: In AC circuits, impedance (Z) replaces resistance. Impedance takes into account both the resistance and reactance (inductive or capacitive) of the circuit. For purely resistive circuits, the impedance is simply equal to the resistance (Z = R).
AC Voltage and Current: In a purely resistive circuit, when AC voltage is applied, the current through the circuit also alternates sinusoidally. The relationship between voltage and current is still governed by Ohm's law (V = I * R), where I and V are instantaneous values of current and voltage.
Power in AC Circuits: In a purely resistive circuit, the power calculations are the same as in DC circuits. The instantaneous power (P) is given by P = V * I, where both V and I are instantaneous values. However, in AC circuits, the voltage and current are changing with time, so the power also varies sinusoidally. The average power over one complete cycle is given by P_avg = V_rms * I_rms * cos(θ), where V_rms is the root mean square voltage, I_rms is the root mean square current, and θ is the phase angle between voltage and current.
Phase Angle: In a purely resistive circuit, the phase angle between voltage and current is zero degrees (θ = 0°). This means that the voltage and current waveforms are in phase with each other.
Power Factor: Power factor (PF) is a measure of how effectively a circuit converts electrical power into useful work. In a purely resistive circuit, the power factor is 1, indicating maximum power transfer and no phase shift between voltage and current.
Series and Parallel Connections: Just like in DC circuits, resistors in AC circuits can be connected in series or parallel. The rules for calculating total resistance, current division, and voltage division remain the same.
Voltage and Current Waveforms: The voltage and current waveforms in a purely resistive AC circuit are both sinusoidal and in phase with each other. The amplitude of the current waveform is determined by the voltage amplitude and the resistance according to Ohm's law.
Phasor Diagrams: Phasor diagrams are graphical representations used to analyze AC circuits. In a purely resistive circuit, the voltage and current phasors are aligned along the same axis, representing zero phase difference.
Understanding purely resistive AC circuits is foundational for grasping more complex AC circuit behaviors involving reactive elements like capacitors and inductors. These fundamentals are essential for designing and analyzing various electrical systems, including power distribution networks and electronic devices.