Electromotive Force and Internal Resistance

1.      Electromotive force V(e.m.f.) of an electrical source is defined as the work done (W) by the source in driving per unit charge around a complete circuit: V(e.m.f.) = W/Q = E/Q.
      a.   A complete circuit consists of both the internal (within the source) and the external circuits (outside the source):

b.       An electrical source can be a cell, a battery or any other source of electricity.

c.      A cell uses chemical reaction to produce current – it converts chemical energy to electrical energy. A cell produces one directional current known as the DC current.

d.       A battery is a combination of 2 or more cells in series.

2.      Since it is energy that enables work to be done, electromotive force V(e.m.f.) can be alternatively viewed as the electrical energy E supplied or used by the source to drive per unit charge around a complete circuit:

                        V(e.m.f.) = W/Q = E/Q

                        V(e.m.f.) = W/It (since, Q = It as I = Q/t)

                        V(e.m.f) = P/I (since power P = W/t)

Therefore, electromotive force may also be defined as the ratio of the total power supplied to the whole circuit to the current flowing through it.

3.      Electromotive force V(e.m.f.) may be measured by:

               i.      A high-resistance voltmeter: By measuring the potential difference of the cell or electrical source in an open circuit – this is however not the true value because a small current still flows through the voltmeter and part of the electromotive force becomes part of the potential difference across the voltmeter itself;

             ii.      A cathode ray oscilloscope; or

            iii.      A potentiometer.

4.      Experimental evidence (pg. 379) shows that:

               i.      Electromotive force V(e.m.f.) is (approximately) the potential difference across the cell or source of electricity in an open circuit – when no current flows through the external circuit or through any external components (Yr 2005 SPM P1 Q38 at pg. 11).

             ii.      Electromotive force V(e.m.f.) is not the same as terminal potential difference Vt – i.e. it is not equal to the potential difference across a closed external circuit through which current is flowing:

V(e.m.f.) > terminal potential difference Vt:

V(e.m.f) > Vt or Vt < V(e.m.f) …(Yr 2011 SPM P1 Q36 at pg. 288)

5.      Lost volt or voltage drop (Vd) refers to: The difference between electromotive force E (or, V(e.m.f.) when circuit is open and terminal potential difference Vt (when circuit is closed) (Vd = V(e.m.f.) – Vt). Lost volt (Vd) is due to the internal resistance r of the cell or electrical source:

V(emf) – Vt = + Vd; or

V(emf) = Vt + Vd; or

Vt = - Vd + V(emf); or
Vt = -rI + V(emf)...(This linear equation is analogous to y = mx + c, y  = Vt; x = I; -r is the gradient m and V(e.m.f.) is the y-intercept of the linear graph)

6.      The internal resistance r of a cell is the resistance within the cell or within the internal circuit – that is, the resistance against the moving charge due to the electrolyte.

                                                                                                                    

7.      To show the existence of internal resistance: A torch is switched on for, say, 20 minutes and the dry cell in the torch becomes hot – due to internal resistance of the cell.

8.      Internal resistance r can be found:

               i.      By finding the voltage drop Vd over the current I flowing when the circuit closed; or

(Yr 2007 SPM P1 Q37 at pg. 100) / (Yr 2010 SPM P1 Q41 at pg. 241); or

             ii.      By finding the gradient of the Vt-I graph,

     where Vt = -rI + V(emf)

    (as in y = mx + c,

    Where, V(emf) is the y-intercept; and

     gradient m = internal resistance -r;

     see the experiment to determine V(emf) and r using the  formula, Vt = -rI + V(emf) at pg. 381)

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Updated By: tutortan1@gmail.com (8/4/12)