Unit 17: Alternating Current — Short Questions

Resistance does not change the value of capacitance itself, but when a resistor is placed in series with a capacitor it combines vectorially with the capacitive reactance X_C to form the impedance Z = √(R² + X_C²) of the RC circuit. It also controls the RC time constant τ = RC, which governs how quickly the capacitor charges or discharges, and it changes the phase angle between voltage and current from the pure-capacitor value of 90° to θ = tan⁻¹(1/ωCR), which is always less than 90°.

Amplitude (peak value, V₀ or I₀) is the maximum value an AC waveform reaches on either the positive or the negative half-cycle, measured from the zero line to that highest point. Peak-to-peak value is the total distance from the positive peak to the negative peak of the waveform. For a symmetrical sine wave, peak-to-peak value is twice the amplitude: V_pp = 2V₀.

In an RC circuit the capacitor charges and discharges through the resistor at a rate governed by the time constant τ = RC, which gives a predictable and adjustable delay before the voltage across the capacitor reaches a certain fraction of the supply voltage. By choosing suitable values of R and C, this fixed, repeatable charging/discharging time can be used to generate precise time delays, pulses, or oscillations, which is why RC circuits form the basis of timing and oscillator circuits.

A choke coil (inductor with very small resistance) limits AC current by means of its inductive reactance X_L = 2πfL, but because the current in it lags the voltage by nearly 90°, its power factor (cosθ) is almost zero, so practically no power is dissipated as heat. A resistor, on the other hand, limits current by dissipating I²R as heat, wasting electrical energy. Hence a choke limits AC current without consuming significant power, making it more efficient than a resistor.

(1) Tuning in radio and television receivers to select a desired station frequency. (2) Band-pass filters in communication devices, allowing signals within a specific frequency range to pass while attenuating others. (3) Induction heating in induction cooktops, where a resonant RLC-parallel circuit generates high-frequency current in a coil to heat metal cookware. (4) Voltage amplification circuits, where at resonance the voltage across the inductor and capacitor becomes much larger than the applied voltage due to the large circulating current.

The energy stored in an inductor is U_L = ½LI², while the kinetic energy of a moving mass is K = ½mv². In this analogy, the current I plays the same role as velocity v, and the self-inductance L plays the same role as mass m: just as mass is a measure of a body's inertia (resistance to change in velocity), inductance is a measure of a coil's "electrical inertia" (its opposition, through back emf, to a change in current). In both cases the stored energy depends on the square of the "flow" quantity (v or I) and can never be negative, confirming the direct analogy between U_L = ½LI² and K = ½mv².

Some safety measures are (1) switch off and disconnect the power supply before working on a circuit; (2) use insulated tools and wear insulated gloves/footwear, never work with wet hands; (3) use fuses, circuit breakers and proper earthing/grounding to protect against overloads and leakage currents; (4) never exceed the current or voltage rating of wires, appliances or protective devices; (5) prefer low-voltage AC supplies where possible, since low-voltage AC is safer to handle and reduces risks; (6) keep AC and DC lines properly isolated from each other.

When the current is switched on, the increasing current produces an increasing magnetic flux through the coil, which by Faraday's/Lenz's law induces a back emf (ε = −L ΔI/Δt) that opposes the applied voltage, so the current rises gradually to its final value instead of jumping instantly. When the current is switched off, the rapidly collapsing flux again induces an emf, but this time it tries to maintain the current in its original direction, which can momentarily produce a large induced voltage (often seen as a spark across the switch contacts).

At 0.1 A the heating produced in the body (I²R) is too small by itself to be lethal. Death is instead caused because this current disturbs the body's own small electrical signals that regulate the heartbeat: the external current interferes with the heart's electrical pulses and can throw the heart out of its normal rhythm (ventricular fibrillation), stopping effective pumping of blood. Thus it is the disruption of the heart's electrical activity, not resistive heating, that makes such currents fatal.