The Internal Resistance of a Cell and Electromotive Force - Lab Report Example

The Internal Resistance of a Cell and EMF Abstract The report below is of determining some features of the dry cell including the electromotive force and internal resistance of the cell. The current values together with the terminal voltage are recorded after connecting the cell in series with a resistor of a lower value. The resistor value was gradually increased to achieve different values of the terminal voltages and the current. A graph of best fit is plotted for terminal voltage against current. The results from the graph are then used to determine the electromotive force of the cell and its internal resistance. Further analysis revealed more features of the dry cell in a circuit. Aim To come up with a design of a circuit to experiment the internal resistance of a dry cell and it’s EMF. Apparatus and Materials Cell, leads of copper insulated wires, several resistors between 10-100Ω, multimeters (2)- one meter is to be used as an ammeter while the other as voltmeter. Theory Electric current can be described as the manner in which the electric charge flow in a circuit in order to transfer energy portions to regions of resistance like resistors, buzzers, or bulbs) in the circuit. The circuit gets the energy at the start of the circuit where dry cells are producing electrical energy from chemical energy. The batteries available in today’s markets are mostly constructed from materials that possess negligibly small internal resistance. Real batteries do not only provide voltage to the circuit but they also offer some internal resistance. Any device that produces the voltage purely is called an electromotive force (E.M.F.) Whichbattery is the total energy that is changed electrical energy during the passage of a unit charge through the production point. It forms a voltage and reflects the total amount of energy supplied through the circuit. The terminal voltage a battery produces at a point without the flow of current is the EMF. The units for measuring EMF is volts (Eppley, 1932). All batteries/cells lose energy as heat when they are dissipating current because of the presence of their internal resistance. The voltmeter is used in the circuit to get the emf values. The addition of a resistor in the circuit drops the reading on the voltmeter to voltage, v. Meanwhile, voltage does not experience full transfer in the circuit but a portion of it is wasted due to the presence of internal resistance within the battery. The dry cell only possesses internal resistance which converts the energy present into heat. Emf= used volts+lost volts E=V+v So we can now redraw the circuit as: The cell forms a perfect cell that is in series with r (internal resistor) Thus EMF= voltage though internal resistor + voltage through R E= v + V Since the entire cell has to be crossed by a voltmeter, E cannot be directly measured including the cell's internal resistance, r. A connection of a voltmeter across the cell measures the terminal p.d. Ohm’s law provides that V= IR, while at the same time v = Ir It give us E= I(r + R) From the previous formulas, the voltage above is smaller compared to the emf by Ir. Lost voltage is tabulated from Ir. From the last equation above, terminal voltage, p.d. = EMF-Lost voltage V= E -Ir The dry cell's EMF together with its internal resistance can alternatively be calculated by other methods. A plot of terminal voltage versus current can help achieve the above. V varies inversely with changes in I to produce a straight line graph. The line equation of y=mx+c, is applicable to the formula of electromotive force, E= Ir (Glaize, 2013). If we plot current values on the x-axis and the voltage values on the y-axis, then the intercept (c) on the y-axis equals the EMF while gradient (M) of the graph equals internal resistance, r, of the dry cell (Glaize, 2013). Most people usually have a notion that the electromotive force of a battery usually remain fixed in value. The reason being, only the chemical reactions within the battery are believed to be the only processes occurring within the battery. Current withdrawn from the battery increases with a decrease the battery voltage. The voltage and EMF are only equal at the point where the current values are excessively small. A critical value of current exists where the current withdrawn from battery cannot exceed. Thus, Io= E/ r. It follows that if we use a conducting wire of negligible resistance in short-circuiting a battery, r of the dry cell limits the current drawn from the battery. The maximum amount of current, Io that can possibly be drawn is achieved. Real battery can be characterized with regard to its emf, E which is the voltage when no I is flowing in the circuit, together with the current Io supplied by the voltage (Glaize, 2013). Torches and calculators are powered by a dry cell with a standard value of 1.5V and 0.1A. Short-circuiting the dry cell would thus cause no greater problems. The dry cell is drained off its power at a faster rate while the current flowing won't be dangerously large. A car battery is supposed to have smaller internal resistance compared to a dry cell due to the ratings of the car battery at 12v, 200A. If someone accidentally short-circuits a car battery, the results will be fairly catastrophic (Walden, 1924). Procedure A circuit was set up with the battery, ammeter and resistor in series. A voltmeter was then connected to measure the potential difference across the cell terminals. Voltmeter readings were recorded in the results table. There were also recordings of the terminal p.d. and the current in the circuit alongside a note of the resistor. The resistor was replaced with one of a different resistance and the readings taken. The procedure above was repeated for nine different resistors. Lastly, the precision of the meters were recorded. Discussion and Results Resistance (Ω) Terminal p.d. V(v) Current, I(A) Mean Terminal p.d. V(v) Mean Current, I(A) 100 6.75 5.38 4.34 0.067 0.053 0.043 5.49 0.054 200 6.84 5.93 5.33 0.034 0.029 0.026 6.03 0.029 430 6.87 6.45 6.07 0.016 0.015 0.014 6.46 0.015 560 6.86 6.53 6.24 0.012 0.011 0.011 6.54 0.011 680 6.87 6.60 6.36 0.010 0.009 0.009 6.61 0.009 750 6.88 6.63 6.40 0.009 0.008 0.008 6.64 0.008 820 6.88 6.65 6.43 0.008 0.008 0.007 6.65 0.007 910 6.88 6.66 6.47 0.007 0.007 0.007 6.67 0.007 1000 6.88 6.70 6.51 0.006 0.006 0.006 6.70 0.006 Precision of the ammeter = 0.0024% Precision of the voltmeter = 0.0024% Safety Precautions 1. The battery should either be switched off or disconnected between the readings of the values of the terminal voltage and the current. 2. Care should be exercised to never be short-circuit terminals cell terminals. 3. Always begin the experiment with a smaller load. 4. A single multimeter should be used as an ammeter and the other as a voltmeter without interchanging the two. From the graph of terminal potential difference (V) against the current in the circuit (I), we obtain a straight line graph. We can then arrange the e.m.f. equation from above to match the general expression for a straight line, y=mx+c. Thus, E=V+Ir, becomes E-Ir=V V=E-Ir When compared with the equation of a straight line, V and I form the y and x axes respectively while the slope/gradient of the graph becomes the r. E forms the y-intercept. The y-intercept that is the emf of the cell= 7.0 v The gradient (m) of the graph= (y2-y1)/(x2-x1) = (6.03-7.00)/(0.029-0) =33.45 The internal resistance of the dry cell is 33.45Ω Conclusion and Recommendations The results show that there was voltage reduction due to an increase in the circuit resistance arising from the additional resistance. The values obtained from the experiment don’t form a straight line graph as it should be. A straight line drawn from the best-fitting line has y-intercept. The prediction from the research done earlier together with the knowledge previously in place were proven to be accurate. Terminal voltage decreases gradually in accordance to Ohm’s law. The graph indicates that both the emf and internal resistance can be calculated for the dry cell. The EMF, E, is obtained from the intercept on the y-axis whereas internal resistance, r, can be derived from gradient of the best-fitting line (Eppley, 1932). Lower resistor values caused a variation in the internal resistance. The rise in the internal resistance is as a result of increase in current resulting from low overall resistance. From the observation, it can be noted that the internal resistance should not be viewed as an extra resistor found within the dry cell. There is an efficient transfer of energy because the external resistance is excessively large when compared to the internal resistance. (Walden, 1924). The problems encountered while performing the experiment were mainly from the equipment used in getting the data. The values plotted could not provide a straight line graph due to some variations in instrument reproducibility features. A line of best fit was thus drawn to achieve the required objectives and valid conclusions. The final results can be accurate enough when more precise and well-functioning equipment replaces the ones used. A decision to take more readings from the ammeter and the voltmeter would help provide more accurate data since more values would be available for plotting. Reference List Eppley, M. (1932). International standard of electromotive force. Electr. Eng., 51(5), pp.341-343. Glaize, C. and Genies, S. (2013). Lithium batteries and other electrochemical storage systems. Hoboken: Wiley. Walden, G. (1924). An improved method for measuring the elctromotive force of cells with high internal resistance. [Poughkeepsie, N.Y.]: [Lansing-Broas Print. Co.]. Read More