Electromotive force and internal resistance
Section: D.C. Circuits | Syllabus: Cambridge AS Level Physics 9702
Electromotive Force (e.m.f.) Electromotive Force (e.m.f.) The energy transferred per unit charge by a source in driving charge around a complete circuit. = fraction where = e.m.f. (V), W = work done/energy transferred (J), Q = charge (C) Important Despite its name, electromotive force is NOT a force .
It is measured in volts (V) and represents energy per unit charge, just like potential difference. The term is historical and predates our modern understanding of electricity. Physical Meaning The e.m.f.
of a source tells us how much energy (in joules) is transferred to each coulomb of charge that passes through it. This energy comes from: Chemical energy in cells and batteries Mechanical energy in generators Light energy in solar cells Thermal energy in thermocouples Worked Example: Calculating e.m.f.
Problem: A battery transfers 54 J of energy when 6 C of charge passes through it. What is the e.m.f. of the battery? Solution: = fraction = fraction = 9 V E.m.f. vs Potential Difference Both e.m.f. and p.d.
are measured in volts, but they describe different energy transfers: Property Electromotive Force (e.m.f.) Potential Difference (p.d.) Definition Energy transferred TO each coulomb by the source Energy transferred BY each coulomb in a component Energy conversion Other forms → electrical energy Electrical energy → other forms Where it applies Sources (cells, batteries, generators) Components (resistors, lamps, motors) Symbol (epsilon) V Energy Perspective As charge moves around a circuit: it gains electrical potential energy when passing through the source (equal to the e.m.f.
× charge), and loses this energy when passing through external components (equal to the p.d. × charge). By conservation of energy, the total energy gained equals the total energy lost. Internal Resistance Every real source of e.m.f.
has some internal resistance , denoted r. This is caused by the resistance of the materials inside the source (wires, electrodes, electrolyte, etc.). Internal Resistance The resistance within a source of e.m.f.
that causes energy to be dissipated inside the source when current flows. FIG 10.15: Real Cell with Internal Resistance Show a cell represented as two parts within a dashed box: an ideal e.m.f. source (ε) in series with an internal resistance (r).
This is connected to an external resistance (R). Label the current I flowing through the circuit, the terminal p.d. (V) across the external resistance, and the "lost volts" (Ir) across the internal resistance.
Effect of Internal Resistance When current flows through a source, some energy is dissipated as heat inside the source due to its internal resistance. This reduces the useful energy available to the external circuit.
Energy dissipated inside source per second = I^2r This is why batteries become warm during use Phone chargers become warm because of internal resistance in both the charger and the phone battery The Potential Divider Model A useful way to understand internal resistance is to treat the cell as a potential divider.
The internal resistance r and external resistance R are in series, so the e.m.f. divides between them: FIG 10.16: Cell as a Potential Divider Show two circuit representations side by side: (a) A cell within a dashed box showing e.m.f.
ε with internal resistance r inside, connected to external resistance R. (b) The equivalent potential divider: e.m.f. ε at the top, with r and R in series below it, showing that the p.d. across R (terminal p.d.) is a fraction of ε determined by the ratio R/(R+r).
Using the potential divider principle: V_R = fraction × This shows that the terminal p.d. is always less than the e.m.f. (unless r = 0, which is impossible for real sources). The larger the internal resistance relative to external resistance, the greater the "lost" fraction of the e.m.f.
Terminal Potential Difference The terminal p.d. is the p.d. measured across the terminals of a source when current is flowing. It equals the p.d. across the external circuit. The Key Equation Applying Kirchhoff's second law to a circuit with e.m.f.
, internal resistance r, and external resistance R: E.m.f. Equation = V + Ir Or equivalently: = IR + Ir = I(R + r) where: = e.m.f. of source (V) V = terminal p.d. (V) I = current (A) r = internal resistance (Ω) R = external resistance (Ω) Rearranging: Terminal p.d.
= e.m.f. − lost volts V = - Ir Lost Volts The quantity Ir is called the lost volts or lost p.d. It represents the energy per coulomb dissipated inside the source. The larger the current, the greater the lost volts, and the lower the terminal p.d.
Special Cases When I = 0 (open circuit): V = . The terminal p.d. equals the e.m.f. when no current flows. When R = 0 (short circuit): I = /r (maximum current). All energy is dissipated in the internal resistance - dangerous!
As current increases: Terminal p.d. decreases because lost volts (Ir) increases. Worked Example: Internal Resistance Problem: A battery has e.m.f. 12 V and internal resistance 0.5 Ω. It i…
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