in a Closed Electric Circuit Figure A.3 shows three resistances connected in series with a battery source of 48 V. We define a closed circuit as one in which current flows; an open circuit is a circuit in which no current flows. Figure A.3a is a closed circuit (i.e., the switch is in the closed position) and A.3b is an open circuit (i.e., the switch is in the open position). Emf is measured with a voltmeter, as shown in Figure A.4, where the open circuit voltage (emf) of a battery is measured. A voltmeter is also used to measure potential drop as shown in Figure A.3a. Here the voltmeter is connected across R3 (across points y and z). In later discussion we will also call this the IR drop. Remember Ohm's law: E = IR. Regarding the potential drop across R3, if we know the resistance of R3 and we know the current passing through it, we know the potential or IR drop. This is one of the many applications of Ohm's law. In Figure A.3a, if we measure the potential drop (IR drop) in volts across each resis- tance and sum the values, this will equal the value of the battery emf in the closed circuit condition. Example of Series Resistances. Four resistors are connected in series. Their resistance values are 250, 375, 136, and 741 S2. Suppose we were to replace these four with just one resistor. The current through the circuit will be the same for one or for the four resistors in series. What will be the value in ohms of the single replacement resistor? Voltmeter Switch in closed position Figure A.3a A closed circuit showing three resistances in series with a battery as an emf source. A voltmeter is placed across R3, which measures the potential difference across that resistance. Switch in open position Figure A.3b An open circuit with three resistances in series with emf source. A.3 OHM'S LAW Positive electrode Metal case = negative electrode Figure A.4 Measuring the voltage of a battery. (a) A typical dry cell. (b) Showing voltage measurement using the standard battery drawing symbol. These are open circuit measurements. 