Alternating Current

7.1 INTRODUCTION

This section introduces the fundamental concept of alternating current (AC) as distinct from direct current (DC). Direct current flows in a constant direction with a steady magnitude, whereas alternating current and voltage vary sinusoidally with time. The common electrical mains supply in homes and offices is an alternating voltage that varies like a sine function over time. The current driven by such a voltage is called alternating current (AC current). AC is preferred over DC for power transmission and distribution because AC voltages can be easily transformed from one voltage level to another using transformers, enabling economical transmission over long distances. AC circuits also exhibit unique characteristics exploited in many devices, such as radio tuning, where the frequency-selective properties of AC circuits are utilized. The section also notes the linguistic redundancy in the terms 'AC voltage' and 'AC current' but acknowledges their universal acceptance. The importance of AC in modern electrical energy systems is emphasized, setting the stage for detailed study of AC circuit behavior in subsequent sections.

• Direct current (DC) flows in one direction with constant magnitude.
• Alternating current (AC) voltage and current vary sinusoidally with time.
• Most electrical energy is transmitted and distributed as AC.
• AC voltages can be efficiently transformed to different voltage levels using transformers.
• AC circuits have special properties used in devices like radios.
• Terminology 'AC voltage' and 'AC current' are widely accepted despite redundancy.
• 📌 Alternating Current (AC): Current that reverses direction periodically and varies sinusoidally with time.
• 📌 Direct Current (DC): Current that flows in one direction with constant magnitude.
• 📌 AC Voltage: Voltage that varies sinusoidally with time.

7.2 AC VOLTAGE APPLIED TO A RESISTOR

This section studies the response of a pure resistor connected to an AC voltage source producing sinusoidally varying voltage v = v_m sin ωt, where v_m is the peak voltage and ω is the angular frequency. Applying Kirchhoff's loop rule to the circuit, the instantaneous current i through the resistor of resistance R is found to be i = (v_m / R) sin ωt = i_m sin ωt, where i_m is the peak current amplitude. This obeys Ohm's law for AC circuits. The voltage and current are in phase, meaning their maxima, minima, and zero crossings occur simultaneously. The current varies sinusoidally with positive and negative values, so the average current over a cycle is zero. However, power dissipation is not zero because power depends on i², which is always positive. The instantaneous power dissipated is p = i² R = i_m² R sin² ωt. The average power over one cycle is (1/2) i_m² R, derived using the trigonometric identity for sin² ωt. To express power in a form analogous to DC circuits, root mean square (rms) or effective values of current and voltage are introduced: I = i_m / √2 and V = v_m / √2. The average power then becomes P = I² R = V I, similar to DC power formulas. The section includes a solved example calculating resistance, peak voltage, and rms current for a light bulb rated at 100 W on a 220 V supply.

• AC voltage applied to resistor: v = v_m sin ωt.
• Current through resistor: i = i_m sin ωt, with i_m = v_m / R.
• Voltage and current are in phase in a pure resistor.
• Instantaneous power: p = i² R = i_m² R sin² ωt.
• Average power over a cycle: P = (1/2) i_m² R.
• Root mean square (rms) values defined as I = i_m / √2 and V = v_m / √2.
• Power expressed as P = I² R = V I, analogous to DC power.
• 📌 Root Mean Square (rms) Current: The effective value of AC current producing the same heating effect as DC current.
• 📌 Ohm's Law for AC: i = v / R applies for resistors with AC voltage.
• 📌 Instantaneous Power: Power at any instant, p = i² R for resistors.