Internal Resistance

electromotive force revisited Remember the e.m.f.(ε) is the amount of energy given by the cell to each coulomb of charge passing through it. It is measured in volts Where ε is the e.m.f. (V) E is the energy given (J) Q is the charge (C)

Question A cell has an e.m.f. of 1.5V. How much energy is produced by the cell in one second if a current of 50mA flows 50mA = (50 x 10 -3) Cs -1 So in 1 second 50 x C flows E= 0.75J in one second

terminal p.d. and e.m.f. V Voltmeter with a very high resistance When a voltmeter with a very high resistance is connected to the teminals of a cell which is not supplying current (unloaded) the voltmeter measures the cell,s e.m.f. A voltmeter with lower resistance can draw a measurable current. The potential difference measured at the terminals of a cell is called the terminal p.d. This is the e.m.f only. when no current flows

Terminal p.d. When a cell is connected in series with a resistor, the terminal p.d. goes down. 1.5V1.42V The e.m.f of the cell is 1.5V R The cell is loaded. The terminal p.d. has now reduced to 1.42V. The e.m.f. of the cell is still 1.5V This voltmeter is measuring the p.d. across the external resistance R

Internal resistance Every component in a circuit has resistance this includes cells. When a current is flowing through the cell there some potential drop in the cell itself because of this internal resistance. r The cell with its internal resistance is often represented in this way and the internal resistance of the cell is represented with a lower case r.

Internal resistance r The total resistance in this circuit is really (R +r) R

Internal resistance The potential difference over R was measured as 1.47V What has happened to the other 0.03V? r R 1.47V r 1.50V The e.m.f. is 1.50V (remember no current is flowing through r here) 0.03V ε= p.d. over R + p.d. over r

Internal Resistance the e.m.f. of the loaded cell is also being used to overcome internal resistance within the cell. r R I ε = p.d. over R + p.d. over r ε=V R + V r As V R = IR and V r = Ir ε= I R + I r ε= I( R +r)

Energy, Terminal p.d. and e.m.f. The e.m.f. is the total energy given to each coulomb of charge. This energy is transferred as heat through every resistance in the circuit (including the internal resistance of the cell). V is the terminal p.d. It is the energy left after some has been transferred in the cell itself. The remaining energy E external is transferred as heat by resistances outside of the cell.

Measuring the internal resistance of a cell ε= V R + V r ε = V + Ir V=(-r)I +ε This is f the form y=mx+c I Gradient = -r V

Measuring the internal resistance of a cell r R V A R R 1.Measure the e.m.f of a cell. 2.Connect,one at a time 6 100Ω resistors in parallel measuring the terminal voltage each time. 3.Plot a graph of V/I. Find the internal resistance by calculating the gradient. The intercept on the Y axis is the e.m.f. of the cell