Alternating Current: Comprehensive NEET Physics Notes

1. Introduction to Alternating Current (AC)

Alternating current (AC) is an electric current that reverses its direction periodically, unlike direct current (DC), which flows in only one direction. AC is the form of electric power delivered to businesses and residences. Understanding the properties and behavior of AC is essential for various applications, including the design of electrical circuits, power transmission, and the operation of household appliances.

Did You Know?

Nikola Tesla was instrumental in the development and widespread adoption of alternating current for power transmission, which led to the electrification of entire cities.

2. Basics of AC

2.1 Sinusoidal AC

The most common form of alternating current is sinusoidal. The voltage (or current) in a sinusoidal AC circuit varies with time as:

$v(t)=V_m\sin (\omega t+\varphi )$

Where:

• VmV_mVm​ is the peak voltage,
• ω\omegaω is the angular frequency, and
• ϕ\phiϕ is the phase angle.

The angular frequency $\omega$ is related to the frequency $f$ of the AC as:

$\omega =2\pi f$

2.2 Instantaneous and RMS Values

The instantaneous value of an AC signal is the value at any given moment, while the root mean square (RMS) value is a measure of the effective value of the AC voltage or current. The RMS value for a sinusoidal AC is given by:

$V_{\text{rms}}=\frac{V_m}{\sqrt{2}}$

Similarly, for current:

$I_{\text{rms}}=\frac{I_m}{\sqrt{2}}$

Common Misconception:

Some students confuse the peak value with the RMS value. Remember that RMS is always lower than the peak value for a sinusoidal AC.

Visual Aid Recommendation:
Include a diagram of a sinusoidal wave, marking the peak, RMS, and instantaneous values. This helps in visualizing how AC varies over time.

Quick Recap:

• AC voltage/current varies sinusoidally over time.
• RMS value provides a measure of the effective voltage/current.
• The peak value is higher than the RMS value by a factor of $\sqrt{2}$​.

3. AC Circuit with Resistor

3.1 Voltage and Current in a Resistive Circuit

In a purely resistive AC circuit, the current and voltage are in phase. The relationship between voltage and current is given by Ohm’s law:

$V(t)=IR(t)$

Where $R$ is the resistance. The power consumed in the resistor is:

$P=I_{\text{rms}}^{2}R$

Real-life Application:

Resistors are used in devices like electric heaters, where electrical energy is converted into heat energy due to the resistance.

Quick Recap:

• In resistive AC circuits, voltage and current are in phase.
• Power is dissipated in the form of heat.

4. AC Circuit with Inductor

4.1 Voltage and Current in an Inductive Circuit

In a purely inductive AC circuit, the current lags behind the voltage by 90° (or $\frac{\pi }{2}$ radians). The voltage across the inductor is given by:

$V(t)=L\frac{dI(t)}{dt}$

Where LLL is the inductance. The reactance of the inductor is:

$X_L=\omega L$

The power factor in an inductive circuit is zero, meaning no real power is consumed, only reactive power.

Common Misconception:

Students often confuse the phase difference in inductive circuits. Remember, current lags voltage by 90° in an inductive circuit.

Visual Aid Recommendation:
Include a phasor diagram showing the relationship between voltage and current in an inductive circuit. This aids in understanding the phase difference.

Quick Recap:

• In an inductive circuit, current lags behind voltage by 90°.
• Inductive reactance depends on frequency and inductance.

5. AC Circuit with Capacitor

5.1 Voltage and Current in a Capacitive Circuit

In a purely capacitive AC circuit, the current leads the voltage by 90° (or $\frac{\pi }{2}$​ radians). The voltage across the capacitor is given by:

$V(t)=\frac{1}{C}\int I(t)dt$

Where $C$ is the capacitance. The reactance of the capacitor is:

$X_C=\frac{1}{\omega C}$

Just like in the inductive circuit, the power factor is zero, with no real power consumption.

Real-life Application:

Capacitors are used in AC circuits for applications like power factor correction and filtering in electronic devices.

Quick Recap:

• In a capacitive circuit, current leads voltage by 90°.
• Capacitive reactance decreases with increasing frequency.

6. LC Oscillations

6.1 Resonance in LC Circuits

An LC circuit consists of an inductor and a capacitor. At resonance, the inductive reactance equals the capacitive reactance:

${\omega }_0=\frac{1}{\sqrt{LC}}$

At resonance, the circuit can oscillate freely, and the energy oscillates between the magnetic field of the inductor and the electric field of the capacitor.

Common Misconception:

Students often think resonance only occurs in mechanical systems. However, electrical circuits can also resonate when inductive and capacitive reactances cancel each other out.

Visual Aid Recommendation:
Include a diagram showing the energy exchange between the capacitor and inductor in an LC circuit.

Quick Recap:

• Resonance in an LC circuit occurs when inductive and capacitive reactances cancel each other.
• Resonance frequency depends on the values of inductance and capacitance.

7. LCR Circuit and Resonance

7.1 Series LCR Circuit

In a series LCR circuit (comprising a resistor, inductor, and capacitor), the total impedance is given by:

$Z=\sqrt{R^2+(X_L-X_C{)}^2}$

The phase angle ϕ\phiϕ between the current and voltage is:

$\tan \varphi =\frac{X_L-X_C}{R}$

At resonance, $X_L=X_C$​, and the impedance is purely resistive.

Real-life Application:

LCR circuits are used in tuning radios and other devices to select specific frequencies.

Visual Aid Recommendation:
Include a phasor diagram for a series LCR circuit at resonance, showing how the current and voltage vectors align.

Quick Recap:

• A series LCR circuit shows different behavior depending on the frequency of the applied AC.
• At resonance, the circuit has minimum impedance, and the current is maximum.

8. Power in AC Circuits

8.1 Power in a General AC Circuit

The average power consumed in an AC circuit is given by:

$P_{\text{avg}}=V_{\text{rms}}{I}_{\text{rms}}\cos \varphi$

Where $\cos \varphi$ is the power factor, indicating how much of the power is used for useful work.

Real-life Application:

Power factor correction is used in industrial settings to improve the efficiency of power usage, reducing energy costs.

Quick Recap:

• Power in AC circuits depends on the RMS values of voltage and current and the power factor.
• The power factor determines the efficiency of power usage in AC circuits.

9. Practice Questions

1. Calculate the RMS value of an AC voltage with a peak value of 230 V.
2. What is the power consumed in a resistor of 10 Ω connected to an AC source with a current of 5 A?
3. In an LCR circuit, if the inductive reactance is 50 Ω and the capacitive reactance is 30 Ω, what is the impedance of the circuit with a resistance of 20 Ω?
4. Explain why the current leads the voltage in a capacitive circuit.
5. Determine the resonance frequency of an LC circuit with L = 2 H and C = 1 μF.

These enhanced notes on alternating current are designed to improve understanding with detailed visual aids, better explanations, and additional NEET-focused practice questions. This content ensures thorough preparation for NEET by covering all essential concepts with clarity and relevance.