Chapter 27: Alternating Currents

The instantaneous values of current and voltage follow mathematical expressions involving peak amplitude and angular frequency, allowing precise description of oscillating electrical signals. Measurement of alternating signals requires specialized instrumentation such as cathode-ray oscilloscopes, which display time-varying waveforms and allow determination of key characteristics including period, frequency, and peak voltage through calibrated horizontal and vertical sensitivity settings. A central challenge in analyzing alternating current circuits involves calculating power, since both current and voltage continuously fluctuate. Root-mean-square values provide a practical solution by defining equivalent steady-state parameters that would deliver identical power to a resistive load compared to the actual alternating signal. The relationship between peak and root-mean-square values follows a fixed mathematical ratio, with average power in resistive loads being exactly half the maximum instantaneous power. Many practical applications require conversion from alternating to direct current through rectification processes. Half-wave rectification uses a single diode to block current during negative cycles, producing pulsating direct current with significant gaps. Full-wave rectification employs a bridge configuration of four diodes to redirect reversed current, maintaining unidirectional flow through the load during both halves of the input cycle. The rectified output contains substantial ripple and fluctuation, necessitating smoothing through capacitive filtering. A capacitor connected across the load resistor charges during peak voltage periods and discharges gradually during voltage drops, dramatically reducing voltage ripple. The effectiveness of smoothing depends on the circuit time constant, determined by capacitance and resistance values, which must exceed the period between successive voltage peaks to prevent excessive discharge between cycles.