Alternating Current mind map

Alternating Current: what the chapter covers

The main idea of each topic with its first key points. Open a branch above for everything, or read the full notes.

1. 1Chapter Overview

   Alternating Current studies current and voltage that vary periodically with time, usually sinusoidally. The chapter begins with AC fundamentals such as waveform, time period, frequency, angular frequency, peak value, mean value, RMS value and phase difference. It then explains how a resistor, inductor and capacitor behave separately in AC circuits using resistance, inductive reactance and capacitive reactance. Series LCR circuits combine all three and show resonance when inductive and capacitive effects cancel. Power factor explains how effectively AC power is used and why some current may be wattless. Finally, transformers apply mutual induction to step voltage up or down. For NEET, this chapter is formula-rich and frequently tests RMS values, reactance, resonance, power and transformer ratios.

   • NEET often asks direct formulas from RMS values, reactance, impedance and transformer relations.
   • AC analysis requires both magnitude and phase, so phasors are very useful.
   • Inductor and capacitor do not consume average power in ideal pure AC circuits.
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2. 2AC Fundamentals

   Alternating current and voltage change magnitude and direction periodically with time. In most circuits, they are represented by sine or cosine functions such as I = I0 sinωt and V = V0 sinωt. A complete repetition is one cycle, whose duration is the time period T. Frequency f is the number of cycles per second, and angular frequency is ω = 2πf. Since AC changes continuously, useful values include peak, RMS and mean values. RMS value is most important because it gives the equivalent DC heating effect. Mean value over a full cycle of symmetrical AC is zero, while mean over a half cycle is non-zero. Phase difference tells how much one AC quantity leads or lags another.

   • Peak value is maximum instantaneous value.
   • RMS value is used in heating, power and household AC ratings.
   • Mean value over half cycle of sine wave is 2I0/π.
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3. 3AC in Resistor, Inductor & Capacitor

   A resistor, inductor and capacitor respond differently to alternating current. In a pure resistor, current and voltage are in the same phase and energy is dissipated as heat. In a pure inductor, voltage leads current by 90° because the inductor opposes change in current; its opposition is inductive reactance XL = ωL. In a pure capacitor, current leads voltage by 90° because current is maximum when voltage changes fastest; its opposition is capacitive reactance XC = 1/ωC. These phase relations are best represented by phasor diagrams, where rotating vectors show relative phase. Ideal inductor and capacitor do not consume average power over a full cycle.

   • Reactance has unit ohm, like resistance.
   • Inductive reactance increases with frequency.
   • Capacitive reactance decreases with frequency.
   Read AC in Resistor, Inductor & Capacitor notes

4. 4LCR Circuits & Resonance

   A series LCR circuit contains resistance, inductance and capacitance connected in series with an AC source. The resistor voltage is in phase with current, inductor voltage leads current by 90°, and capacitor voltage lags current by 90°. Their combined opposition is impedance, Z = √[R² + (XL - XC)²]. Resonance occurs when XL = XC, so inductive and capacitive reactances cancel. At resonance, impedance becomes minimum and equal to R, current becomes maximum, phase difference becomes zero and power factor becomes one. Resonance frequency is f0 = 1/(2π√LC). The quality factor describes sharpness of resonance. Resonance is used in radio tuning, filters and frequency selection circuits.

   • LCR resonance occurs only when inductive and capacitive effects cancel.
   • At low frequency, capacitive reactance dominates.
   • At high frequency, inductive reactance dominates.
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5. 5Power Factor

   Power factor tells how effectively an AC circuit converts supplied electrical energy into useful work. In an AC circuit, voltage and current may have a phase difference ϕ. Average power consumed is Pavg = VrmsIrms cosϕ, where cosϕ is the power factor. If voltage and current are in phase, cosϕ = 1 and power use is maximum. If phase difference is 90°, as in an ideal inductor or capacitor, average power is zero and current is called wattless current. In practical circuits, low power factor increases current for the same useful power, causing greater transmission loss I²R. Power factor correction uses capacitors or suitable devices to reduce phase difference and improve efficiency.

   • Power factor is dimensionless.
   • Only the in-phase component of current contributes to average power.
   • Reactive current circulates energy between source and reactive elements.
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6. 6Transformers

   A transformer is an AC device that changes voltage using mutual induction. It consists of primary and secondary coils wound on a laminated soft iron core. When AC flows in the primary coil, it produces changing magnetic flux in the core. This changing flux links the secondary coil and induces an emf according to Faraday’s law. In an ideal transformer, Vs/Vp = Ns/Np and input power equals output power, so VpIp = VsIs. A step-up transformer has more turns in the secondary and increases voltage while decreasing current. A step-down transformer has fewer secondary turns and decreases voltage while increasing current. Practical transformers have losses due to copper resistance, eddy currents, hysteresis and flux leakage.

   • Transformer changes voltage but not frequency.
   • Soft iron core provides a low reluctance path for magnetic flux.
   • Primary coil receives input AC; secondary coil delivers output AC.
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