CBSE Class 12 || Physics || Alternating Current || Part-I || Animation || in English

A conversation unfolds about how laptops, which operate on DC voltage due to their batteries, can charge using an AC power supply. The explanation reveals that the laptop charger converts alternating current (AC) into direct current (DC), enabling smooth operation of devices designed for DC usage. This process highlights a fundamental principle of electrical appliances and introduces the topic of alternating currents.

Alternating current (AC) is defined as an electric current that periodically reverses direction, unlike direct current (DC), which flows in one constant direction. The differences between AC and DC are highlighted by their flow characteristics and applications. Calculations involving AC voltage applied to resistors, inductors, or capacitors require understanding of root mean square values for both voltage and current. Inductive reactance describes the opposition offered by an inductor to changes in AC while capacitive reactance refers to a capacitor's resistance against such variations.

An AC generator produces a sinusoidal alternating voltage over time, known as AC voltage. The current it drives in circuits is called AC current. Most household electrical appliances and main power supplies rely on this type of voltage due to its efficiency and ease of transformation for various applications.

Alternating current (AC) or voltage is characterized by periodic variations where each cycle consists of equal positive and negative halves. For AC, the direction of current reverses every half-cycle, while for alternating voltage, the polarity switches correspondingly. These cycles are symmetrical with consistent amplitude on both sides throughout all cycles.

Alternating Current (AC) cannot produce chemical effects like electroplating or electrolysis, whereas Direct Current (DC) can. Transformers are effective for stepping up or down the voltage of AC but have no utility with DC. Conversion between these currents is possible: electronic rectifiers convert AC to DC, while inverters transform DC into AC.

In an AC circuit with a resistor, the voltage across the source varies sinusoidally as v = Vm sin(ωt), where Vm is the amplitude of alternating voltage and ω is angular frequency. Applying Kirchhoff's rule gives current i = (Vm / R) sin(ωt), showing that maximum current equals Vm/R. The instantaneous voltage across the resistor Vr can be expressed as Vr = IR, which simplifies to Vr = Vm sin(ωt). This demonstrates that in such circuits, current through a resistor remains perfectly in phase with its terminal voltage.

In sinusoidal circuits, voltage and current alternate between positive and negative values over a cycle, resulting in an average value of zero. The root mean square (RMS) value provides a meaningful measure by taking the square root of the average squared values. For current, Irms equals Im divided by √2 or approximately 0.707Im; similarly for voltage Vrms equals Vm divided by √2 or about 0.707Vm. In purely resistive circuits, resistance remains constant across all frequencies as depicted by a horizontal line on a graph plotting resistance against angular frequency.

To determine the instantaneous voltage in a household electrical system marked 220 volts and 50 hertz, we start by calculating peak voltage (E₀). Using E₀ = √2 × EV, where EV is the effective voltage of 220V, results in E₀ = 311 volts. Next, angular frequency ω is calculated using ω = 2πν with ν as frequency (50 Hz), yielding ω ≈ 314 radians/second. The equation for instantaneous voltage becomes e(t) = 311 sin(314t).

The instantaneous power delivered to a resistor is calculated as the product of voltage and current, expressed mathematically as P_r = V_m * I_m * sin²(ωt). Over one complete cycle, the average power simplifies due to the time-averaged value of sin²(ωt) being 1/2. This results in an expression for average power: P_r = (V_RMS)(I_RMS), or equivalently, P_r = I_RMS² * R.

The phase relationship between current and voltage in an AC circuit is determined using phasors, which are rotating vectors representing sinusoidal variations over time. Phasor diagrams visually depict these relationships, with vector lengths corresponding to maximum voltage (Vm) and current (Im). In a resistor-based AC circuit, the phasors for voltage (V) and current (I) remain co-linear as they rotate because both are in phase. At any given moment t, the angle formed by these phasors with the positive x-axis equals ωt.

When AC voltage is applied to a circuit containing only an inductor, the changing current generates a back electromotive force (emf) proportional to the rate of change of current. Using Kirchhoff's rule and substituting values, it is determined that di/dt equals Vm/L multiplied by sin(ωt). Integrating this equation over time reveals that the oscillating current has a phase difference of -π/2 relative to voltage. The amplitude of this oscillation can be expressed as Im = Vm / (ωL), where ω represents angular frequency.

Inductive reactance, denoted as Xl, is defined by the expression ωL (omega times inductance), playing a role similar to resistance in circuits. The amplitude of current in a purely inductive circuit can be calculated using Im = Vm / Xl. For power delivery, the instantaneous power supplied to an ideal inductor averages out to zero over one complete cycle due to the sinusoidal nature of sine(2ωt).

In an AC circuit with inductance, the current lags behind the voltage by a phase angle of π/2. At points where the current is zero on its graph, it experiences its steepest slope and maximum rate of change. This demonstrates that voltage and current are not synchronized but instead differ in phase by one-quarter wave cycle.

In an AC circuit with a capacitor of capacitance C, the voltage across the source is expressed as V = Vm sin(ωt). The instantaneous voltage across the capacitor (Vc) relates to charge Q by Vc = Q/C. Applying Kirchhoff's rule gives V - Vc = 0, leading to substitution where VC equals Vm sin(ωt). The resulting current in this system oscillates and can be described as I(t) = Im sin(ωt + π/2), with amplitude Im determined by ωCVm.

Capacitive reactance (Xc) is defined as 1 divided by the product of angular frequency (omega) and capacitance (C). The amplitude of current in a purely capacitative circuit can be expressed as either Im = Vm / Xc or Irms = Vrms / Xc. Instantaneous power supplied to a capacitor, calculated using Vm * Im/2 multiplied by sin(2 omega t), averages out to zero over one complete cycle due to the sine function's properties. Consequently, no net power is delivered to an ideal capacitor.

In an AC circuit with a capacitor, the current leads the voltage by 90 degrees (π/2). As voltage rises from point A to B, charge on the capacitor increases and reaches its peak at B. However, maximum positive current occurs earlier during initial charging at A'. When voltage decreases from B to C, charges flow out in reverse direction as indicated by negative current between points B' and C'. This demonstrates that voltage and current are always one-quarter wave cycle out of phase.

The first alternator producing alternating current was a dynamo electric generator, constructed in 1832 by French instrument maker Hippolyte Pixii. It operated based on Michael Faraday's principles of electromagnetic induction. Inductors are incapable of reducing direct current but can reduce alternating current effectively. Capacitors allow the flow of alternating currents while blocking direct currents.

An AC generator produces a sinusoidal alternating voltage that alternates between positive and negative values within each cycle. In an AC circuit, the current through a resistor aligns in phase with the voltage across its terminals. The root mean square (RMS) current is defined as the square root of the average value of squared currents over time. Phasor diagrams represent sinusoidally varying voltages and currents using rotating vectors whose lengths correspond to their maximum values; these are called phasors. Additionally, in inductive circuits, current lags behind voltage by π/2 radians while in capacitive circuits it leads by π/2 radians.