Alternating current – AC

Alternating current is that current which continuously varies in magnitude and periodically reverses it direction. The same is true for alternating e.m.f.

During one cycle, the current (or e.m.f) rises from zero to maximum in one direction, falls to zero, then becomes maximum in the reverse direction and again falls to zero. The number of cycles completed by alternating current in one second is known as frequency of AC. Generally expressed in Hz (hertz) or cps (cycles per second). The household supply of AC in India has a frequency of 50 cycles per second.

When a coil is rotated in a magnetic field, an alternating e.m.f is induced in the coil. At any instant, the e.m.f is given by,

E = E₀ sinωt

where E is the instantaneous value of alternating e.m.f, E₀ is the peak value, nd ωt is the phase of alternating e.m.f.

Phase of alternating e.m.f (or current) may be defined as the fraction of the time period that has elapsed since the e.m.f (or current) last passed its zero value in the positive direction.

If R be the resistance of the circuit, then E/R = (E₀/R) sinωt or I = I₀ sinωt

where I is the instantaneous value of AC, I₀ is the peak value and ωt is the phase of AC.

Average value of A.C over a half cycle : Average or Mean value of alternating current over a half cycle is that steady current which will send the same charge in the circuit in the same time as is sent by alternating current in the same circuit in half time period.

I_m = (2/π)I₀

I_m = 0.637 I₀

The mean value of AC for negative half cycle will come out to be -0.637 I₀. The mean value over a complete cycle of A.C will come out to be zero.

Root Mean Square Value of A.C : Root Mean Square value (rms value) or Virtual value or Effective value of AC is that steady current which would produce the same heat in given resistance in the given time as is done by the alternating current when passed through the same resistance for the same time.

I_rms = .707 I₀

The rms value of AC is .707 times the peak value of A.C.

Principle of A Potentiometer

Principle of Potentiometer :

“The potential difference across any length of a wire of uniform cross-section and uniform composition is proportional to its length when a constant current flows through it.”

Explanation :

The battery in primary circuit creates a potential difference across the length of the potentiometer wire. A potential gradient K is also developed across the wire. (K=Potential supplied by main batterry divided by length of wire). The potentiometer wire is thus a source of variable potential difference. That is, potential depends on length of wire selected. (Potential = length * potential gradient).

The cell in secondary is connected opposite to that in primary. This current opposes the current flowing across the potentiometer. When the both potential, i.e, potential difference across the chosen length of potentiometer wire and potential difference caused by the cell in secondary circuit, becomes equal and opposite, no current flows through the secondary circuit. Thus the galvanometer shows null deflection.

Sensitivity of a Potentiometer :

The sensitivity of the potentiometer depends upon the value of potential gradient K. (K=Potential supplied by main battery divided by length of wire) Smaller the value of K, smaller the potential difference that a  potentiometer can measure and more is the sensitivity of the potentiometer. Thus, for a given potential difference, the sensitivity of the potentiometer increases with the increase in length of potentiometer wire.

? Why Potentiometer is chosen over Voltmeter to measure the potential of a cell?

Ans : When Voltmeter is used, current flows through the circuit, and because of the internal resistance of the cell, always terminal potential will be less than the actual cell potential. But in a potentiometer circuit, when the potential difference is balanced, no current flows in the circuit, so terminal potential will be equal to actual cell potential. i.e, Voltmeter measures the terminal potential of a cell, but Potentiometer measures actual cell potential.

A Poly-divisible Number

Got this thing from the blog of my friend, Gaurav Tiwari. 😀 So I’m just giving the link to his post : 381654729 : An Interesting Number Happened To Me Today/
The post is about the interesting facts about the number 381654729. Its real cool one!!

Electrochemistry – Some imp. points

Electrochemistry is the study of production of electricity from energy released during spontaneous chemical reactions and the use of electrical energy to bring about non-spontaneous chemical transformations. Galvanic cell or Electro-chemical cell – converts chemical energy liberated during a spontaneous redox reaction to electrical energy. Electrolytic cell – external potential > cell potential. A device for using electrical energy to carry out non-spontaneous reactions. (here, the usual cell reaction, i.e, spontaneously occuring reaction is reversed). Fuel cell – that one in which an uninterrupted supply of electrical energy is obtained by a continuous supply of reactants and continuous removal of the products of the chemical reaction.

Zn – Cu cell
Zn: Anode: Oxidation: loss of electrons
Zn  –>  Zn²⁺ + 2e
Cu: Cathode: Reduction: gain of electrons
Cu²⁺ + 2e  –>  Cu

Overall reaction:
Zn + Cu²⁺  –>  Zn²⁺ + Cu

cell representation:
Zn / Zn²⁺  //  Cu²⁺ / Cu

Cathode: positively charged
Anode: negatively charged

E_cell = E_right – E_left

elctrons flow from anode to cathode
current flows from cathode to anode (+ve to -ve)

Cell potential : always positive

According to convention, a half cell called Standard Hydrogen Electrode represented by

Pt_(s)/H_2(g)/H⁺_(aq), is assigned a zero potential at all temperatures.

Oxidation at H electrode : +ve electrode potential
Reduction at H electrode : -ve electrode potential

To find out the first day of any Year (Optimised)

Shafeeq sent me this code today eve, and i’m sure it is quite ‘optimised’.. than the previous post : https://goforaplusplus.wordpress.com/2011/09/08/to-find-out-the-first-day-of-any-year/. Since he won’t post it anyway, I am forced to publish it!! Cheers to Shafeeq.. 😀 .. !

/*Find the day of Jan 1 of a year*/
#include <iostream>
using namespace std;

int firstday(int year)
{
//1899 chosen as reference year for convenience.
// Jan 1 of 1899 is Sunday
    int reference_year = 1899;
    int leapcount = 0;
    int yearcount;

    if (year >= reference_year)
        yearcount = year - reference_year;
    else
        yearcount = reference_year - year;

    for (int i = 0, tempyear = reference_year; i < yearcount; i++)
    {
        if ( ((tempyear%4 == 0) && (tempyear%100 != 0)) || tempyear%400 == 0)
        leapcount++;

        if(reference_year < year)
            tempyear++;
        else
            tempyear--;
    }

    if(reference_year <= year)
        return (yearcount + leapcount) % 7;
    else
        return 7-((yearcount + leapcount)%7);
}

int main()
{
    char day[7][10] = {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"};
    int year;
    cout << "Enter year :";
    cin >> year;
    cout << "First day of year " << year << " is " << day[firstday(year)] << endl;
    return 0;
}

Wheatstone bridge

♦ It is an arrangement of four resistances used for measuring one of them in terms of the other three. It was devised by Sir Charles F Wheatstone, a British Physicist in 1833.

WheatStone Bridge Circuit

♦ Wheatstone’s Bridge method is unsuitable for the measurement of very low and very high resistances.

♦ Uses: although the Wheatstone  bridge is widely used with manual adjustment for the zero or null galvanometer reading, it is increasingly used with electronic and mechanical arrangements to make it self-balancing, the measurements then being recorded on a paper chart. In this form, the Wheatstone bridge is the basis for many measurement and control devices used in industry. Any quantity such as temperature, humidity, strain, displacement, liquid level in a tank etc. which can be made to produce change in the value of a resistance can be measured with Wheatstone bridge.

♦ Sensitivity: Greater the galvanometer current due to a small deviation from ‘balance’, the more sensitive is the bridge. The sensitivity of the Wheatstone bridge depends upon the following two factors:
(i)  Relative magnitudes of the resistances in the four arms of the bridge.
(ii) Relative positions of battery and galvanometer.

Prof. Callender has given the following rule for the greater sensitiveness of the Wheatstone’s bridge.
The battery should be so connected that the resistance in series with the resistance to be measured is greater than the resistance in parallel with it.

Maxwell gave the following rule for best arrangement of resistances constituting Wheatstone’s bridge.
Out of the battery and galvanometer, the one having the higher resistance should be connected between the junction of two highest resistances and the junction of the two lowest resistances.

Reference : Comprehensive Physics, Laxmi Publications

Related articles

• Principle of A Potentiometer (goforaplusplus.wordpress.com)

To find out the first day of any Year

Devika gave me this problem to solve today morning and now I guess I have found a solution.. 😀

the optimised version for the same is available here : https://goforaplusplus.wordpress.com/2011/09/08/to-find-out-the-first-day-of-any-year-optimised/

#include <iostream>
#include <math.h>
using namespace std;
#define Y_1900 1
#define YEAR 1900
char week[7][10]={"SUNDAY","MONDAY","TUESDAY","WEDNESDAY","THURSDAY","FRIDAY","SATURDAY"};

int findday(int x)
{
    int y,i;
    y = Y_1900+(x-YEAR);
    for(i=YEAR;i<x;i++)
    {
        if(((i%4==0) && (i%100!=0)) || (i%400==0))
        y++;
    };
    y=y%7;
    return y;
}

int main()
{
    int arg,f;
    cout<<"enter year : ";
    cin>>arg;
    f=findday(arg);
    cout<<"january 1 of "<<arg<<" is "<<week[f];
    return 0;

}

The program works fine if the given year is greater than 1900. I tried to extend this to years less than 1900, but it seems impractical coz there seems to be some logical errors in defining leap years.
Still I am posting the code here, to give you a general idea, how it works!

int a;
a=(YEAR-x)%7;
y=(Y_1900+7)-a;
y=y%7;
for(i=YEAR-1;i>=x;i--)
{
    if(((i%4==0) && (i%100!=0)) || (i%400==0))
    {
        if(y==0)
        y=7;
        y--;
    }
};
y=y%7;
return y;

Optimised and extended versions of the same are welcome.. 😉