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Lesson 8.3 • Competency 8.2 & 8.3Complete Lesson
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EMF, Internal Resistance & Power

Electromotive force (EMF) E = W/Q, internal resistance r, terminal potential difference V = E - Ir (discharge) and V = E + Ir (charging), V-I graphical determination of E and r, electrical power dissipation P = VI, and the Maximum Power Transfer Theorem.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • Distinguish between source Electromotive Force (EMF) and terminal Potential Difference (PD).
  • Analyze terminal voltage behavior during discharge (V = E - Ir) and battery recharging (V = E + Ir).
  • State and prove the Maximum Power Transfer Theorem (R_load = r => P_max = E²/(4r)).

Core Theory & Concepts

A battery or electrical source maintains a potential difference by driving charges from lower to higher potential through chemical, mechanical, or solar work. The total work performed per unit charge is the source EMF. Real sources possess an intrinsic internal resistance r, causing the terminal voltage to sag under load.

Terminal Potential Difference

When delivering current I to an external load: V = E - I r. When being recharged by an external charger: V = E + I r.

V = E - I r \quad (\text{discharge}), \quad V = E + I r \quad (\text{recharge})

Maximum Power Transfer Theorem

Maximum power is delivered to external load R when R equals the source internal resistance r. The maximum power is P_max = E² / (4r).

P_{\max} = \frac{E^2}{4r} \quad \text{when} \quad R_{\text{load}} = r

Common Misconceptions

Misconception

The terminal potential difference of a cell is always equal to its rated EMF.

Physical Clarification:Terminal voltage V only equals EMF E when the circuit is open (zero current, Ir = 0). As soon as current flows, the internal voltage drop Ir reduces V below E.

Syllabus Topic Outline

Competency 8.2 & 8.3
  • 1Concept of Electromotive Force (EMF) as work done per unit charge (E = W / Q)
  • 2Internal resistance r of chemical cells and accumulators
  • 3Terminal potential difference equations: discharging (V = E - Ir) vs charging (V = E + Ir)
  • 4Experimental V vs I characteristic line: y-intercept = E, gradient = -r
  • 5Short-circuit current (I_sc = E / r) and open-circuit voltage
  • 6Maximum Power Transfer Theorem derivation and condition R = r