Home | | Physics 12th Std | Solved Example Problems on Alternating Current (AC) and Circuit

Chapter: 12th Physics : Electromagnetic Induction and Alternating Current

Solved Example Problems on Alternating Current (AC) and Circuit

Physics : Alternating Current: Alternating Current (AC) and Circuit: Solved Example Problems with Answers, Solution and Explanation

RMS value of AC: Solved Example Problems


EXAMPLE 4.18

Write down the equation for a sinusoidal voltage of 50 Hz and its peak value is 20 V. Draw the corresponding voltage versus time graph.

Solution



 

EXAMPLE 4.19

The equation for an alternating current is given by i = 77 sin 314t. Find the peak value, frequency, time period and instantaneous value at t = 2 ms.

Solution

i = 77 sin 314t ; t = 2 ms = 2×10-3 s

The general equation of an alternating current is i = Im sin ωt . On comparsion,

(i) Peak value, Im = 77 A

(ii) Frequency, f = ω/2π = 314 / 2 ×3.14 = 50 Hz

Time period, T = 1/f = 150 = 0 .02 s

(iv) At t = 2 m s,

Instantaneous value,

i = 77sin(314×2×10−3 )

 i = 45.24 A


AC circuit containing only an inductor: Solved Example Problems


EXAMPLE 4.20

A 400 mH coil of negligible resistance is connected to an AC circuit in which an effective current of 6 mA is flowing. Find out the voltage across the coil if the frequency is 1000 Hz.

Solution

L = 400 x 10-3 H; Ieff = 6 x 10-3A

f = 1000 Hz




AC circuit containing only a capacitor: Solved Example Problems


EXAMPLE 4.21

A capacitor of capacitance 102/π µF is connected across a 220 V, 50 Hz A.C. mains. Calculate the capacitive reactance, RMS value of current and write down the equations of voltage and current.

Solution


Quality factor or Q–factor: Solved Example Problems


EXAMPLE 4.22

Find the impedance of a series RLC circuit if the inductive reactance, capacitive reactance and resistance are 184 Ω, 144 Ω and 30 Ω respectively. Also calculate the phase angle between voltage and current.

Solution

XL = 184 Ω; XC = 144 Ω

R = 30 Ω

(i ) The impedance is


Impedance, Z = 50 Ω

(ii) Phase angle is


φ = 53.1

 

EXAMPLE 4.23

A 500 μH inductor, 80/π2 pF capacitor and a 628 Ω resistor are connected to form a series RLC circuit. Calculate the resonant frequency and Q-factor of this circuit at resonance.

Solution

L=500×10-6H; C = 80/π2 ×10−12 F; R = 628Ω

(i) Resonant frequency is


 Q =12.5

 

EXAMPLE 4.24

Find the instantaneous value of alternating voltage υ = 10 sin(3 π×104 t) volt at i) 0 s ii) 50 μs iii) 75 μs.

Solution

The given equation is υ = 10sin (3 π×104 t)


 

EXAMPLE 4.25

The current in an inductive circuit is given by 0.3 sin (200t – 40°) A. Write the equation for the voltage across it if the inductance is 40 mH.

Solution

L = 40 × 10-3 H; i = 0.1 sin (200t – 40º)

XL = ωL = 200 × 40 × 10-3 = 8 Ω

Vm = Im XL = 0.3 × 8 = 2.4 V

In an inductive circuit, the voltage leads the current by 90o Therefore,

v = Vm sin ( ωt +90º)

 v = 2 . 4 sin(200t −40 + 90 º)

v = 2 . 4 sin(200t +50 º)volt


Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
12th Physics : Electromagnetic Induction and Alternating Current : Solved Example Problems on Alternating Current (AC) and Circuit |


Privacy Policy, Terms and Conditions, DMCA Policy and Compliant

Copyright © 2018-2023 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.