Tamil Nadu HSE+2 Physics Electromagnetic Induction and Alternating Current Solutions

No.

Question

Answer

1

What is meant by electromagnetic induction?

Whenever the magnetic flux linked with a closed coil changes, an emf is induced and an electric current flows in the circuit. This phenomenon is called electromagnetic induction.

2

State Faraday's laws of electromagnetic induction.

First law: Whenever magnetic flux linked with a closed circuit changes, an emf is induced in the circuit. Second law: The magnitude of induced emf is equal to the time rate of change of magnetic flux linked with the circuit.

3

State Lenz's law.

The direction of the induced current always opposes the cause responsible for its production.

4

State Fleming's right-hand rule.

Stretch the thumb, index finger and middle finger of the right hand mutually perpendicular to each other. If the index finger points in the direction of the magnetic field and the thumb indicates the direction of motion of the conductor, the middle finger indicates the direction of the induced current.

5

Mention the ways of producing induced emf.

Induced emf can be produced by changing the magnetic field BB, the area AA of the coil or the relative orientation θ\theta of the coil with respect to the magnetic field.

6

What do you mean by self-induction?

When current in a coil changes, the magnetic flux linked with it changes, inducing an emf in the same coil. This phenomenon is known as self-induction.

7

What is meant by mutual induction?

When an electric current passing through a coil changes with time, an emf is induced in a neighbouring coil. This is known as mutual induction.

8

What are step-up and step-down transformers?

A step-up transformer converts alternating current with low voltage into alternating current with high voltage. A step-down transformer converts alternating current with high voltage into alternating current with low voltage.

9

Define average value of an alternating current.

The average value of an alternating current is the average of all values of current over a positive half-cycle or a negative half-cycle.

10

Define RMS value of an alternating current.

The RMS value of AC is the value of steady current (DC) that produces the same amount of heat in a given circuit for a given time as produced by the alternating current flowing through the same circuit for the same time.

11

What are phasors?

A sinusoidal alternating voltage or current represented by a vector rotating about the origin anti-clockwise at a constant angular velocity is called a phasor.

12

Define electric resonance.

When the frequency of the applied AC source equals the natural frequency of an RLC circuit, the current in the circuit reaches its maximum value. The circuit is then said to be in electrical resonance.

13

What is meant by wattless current?

The component of current IRMSsin⁡ϕI_{\text{RMS}}\sin\phi that has a phase difference of π/2\pi/2 with respect to the voltage consumes zero power. This component is called wattless current.

14

Give the definition of power factor.

Power factor is the ratio of true power to apparent power in an AC circuit. It is equal to the cosine of the phase angle cos⁡ϕ\cos\phi between current and voltage.

15

What are LC oscillations?

When energy is supplied to a circuit containing a pure inductor LL and a capacitor CC, energy oscillates back and forth between the magnetic field of the inductor and the electric field of the capacitor, producing electrical oscillations of definite frequency.

Topic

Formula

Application

Magnetic Flux

Φ=BAcos⁡θ\Phi = BA\cos\theta

Calculate magnetic flux through a given surface.

Induced EMF

E=−dΦdt\mathcal{E} = -\frac{d\Phi}{dt}

Determine induced emf when magnetic flux changes with time.

Self-Induction

E=−LdIdt\mathcal{E} = -L\frac{dI}{dt}

Calculate induced emf due to a changing current in a coil.

Mutual Induction

E=−MdIdt\mathcal{E} = -M\frac{dI}{dt}

Find induced emf in a neighbouring coil.

RMS Current

IRMS=I02I_{\mathrm{RMS}} = \frac{I_0}{\sqrt{2}}

Determine RMS current from peak current.

RMS Voltage

VRMS=V02V_{\mathrm{RMS}} = \frac{V_0}{\sqrt{2}}

Determine RMS voltage from peak voltage.

AC Power

P=VRMSIRMScos⁡ϕP = V_{\mathrm{RMS}}I_{\mathrm{RMS}}\cos\phi

Calculate average power in an AC circuit.

Resonance

f0=12πLCf_0 = \frac{1}{2\pi\sqrt{LC}}

Determine the resonant frequency of an LC or RLC circuit.

Concept

Formula

Peak and RMS Current

IRMS=I0/2I_{\mathrm{RMS}} = I_0/\sqrt{2}

Peak and RMS Voltage

VRMS=V0/2V_{\mathrm{RMS}} = V_0/\sqrt{2}

Inductive Reactance

XL=ωLX_L = \omega L

Capacitive Reactance

XC=1/ωCX_C = 1/\omega C

Impedance of RLC Circuit

Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L-X_C)^2}

Current in AC Circuit

I=V/ZI = V/Z

Power Factor

cos⁡ϕ=R/Z\cos\phi = R/Z

AC Power

P=VIcos⁡ϕP = VI\cos\phi

Resonant Frequency

f0=1/(2πLC)f_0 = 1/(2\pi\sqrt{LC})

Concept

Formula

Magnetic Flux

Φ=BAcos⁡θ\Phi = BA\cos\theta

Faraday’s Law

E=−dΦ/dt\mathcal{E} = -d\Phi/dt

Self-Induced EMF

E=−L(dI/dt)\mathcal{E} = -L(dI/dt)

Mutual Induced EMF

E=−M(dI/dt)\mathcal{E} = -M(dI/dt)

RMS Current

IRMS=I0/2I_{\mathrm{RMS}} = I_0/\sqrt{2}

RMS Voltage

VRMS=V0/2V_{\mathrm{RMS}} = V_0/\sqrt{2}

Inductive Reactance

XL=ωLX_L = \omega L

Capacitive Reactance

XC=1/ωCX_C = 1/\omega C

Impedance

Z=R2+(XL−XC)2Z = \sqrt{R^2+(X_L-X_C)^2}

Power Factor

cos⁡ϕ=R/Z\cos\phi = R/Z

AC Power

P=VRMSIRMScos⁡ϕP = V_{\mathrm{RMS}}I_{\mathrm{RMS}}\cos\phi

Resonant Frequency

f0=1/(2πLC)f_0 = 1/(2\pi\sqrt{LC})