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

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 314*t*. Find the peak value, frequency, time period and instantaneous value at t = 2 ms.

Solution

i = 77 sin 314t ; t = 2 ms = 2Ã—10-3 s

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

(i) Peak value, Im = 77 A

(ii) Frequency, *f* = Ï‰/2Ï€ = 314 / 2 Ã—3.14 = 50 Hz

Time period, T = 1/*f* = 150 = 0 .02 *s*

(iv) At t = 2 m s,

Instantaneous value,

*i* = 77sin(314Ã—2Ã—10âˆ’3 )

i = 45.24 A

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

EXAMPLE 4.21

A capacitor of capacitance 102/Ï€ ÂµF 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

EXAMPLE 4.22

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

Solution

XL = 184 Î©; XC = 144 Î©

R = 30 Î©

(i ) The impedance is

Impedance, Z = 50 â„¦

(ii) Phase angle is

Ï† = 53.1

EXAMPLE 4.23

A 500 Î¼H inductor, 80/Ï€2 pF capacitor and a 628 Î© resistor are connected to form a series RLC circuit. Calculate the resonant frequency and Q-factor of this circuit at resonance.

Solution

L=500Ã—10-6H; C = 80/Ï€2 Ã—10âˆ’12 F; R = 628â„¦

(i) Resonant frequency is

Q =12.5

EXAMPLE 4.24

Find the instantaneous value of alternating voltage Ï… = 10 sin(3 Ï€Ã—104 t) volt at i) 0â€†s ii) 50 Î¼s iii) 75 Î¼s.

Solution

The given equation is Ï… = 10sin (3 Ï€Ã—104 t)

EXAMPLE 4.25

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

Solution

L = 40 Ã— 10-3 H; i = 0.1 sin (200t â€“ 40Âº)

XL = Ï‰L = 200 Ã— 40 Ã— 10-3 = 8 â„¦

Vm = Im XL = 0.3 Ã— 8 = 2.4 V

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

*v* = Vm sin ( Ï‰t +90Âº)

*v* = 2 . 4 sin(200t âˆ’40 + 90 Âº)

*v* = 2 . 4 sin(200t +50 Âº)volt

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12th Physics : Electromagnetic Induction and Alternating Current : Solved Example Problems on Alternating Current (AC) and Circuit |

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