Voltages across series resistances83would be increased still further. A third bulb would probably blow out almost right awayafter the string was plugged in.Voltages across series resistancesThe bulbs in the string of Fig. 5-1, being all the same, each get the same amount of volt-age from the source. If there are a dozen bulbs in a 120-V circuit, each bulb will have apotential difference of 10 V across it. This will be true no matter how large or small thebulbs are, as long as they’re all identical.If you think about this for a moment, it’s easy to see why it’s true. Look at theschematic diagram of Fig. 5-2. Each resistor carries the same current. Each resis-tor Rn has a potential difference En across it, equal to the product of the currentand the resistance of that particular resistor. These En’s are in series, like cells ina battery, so they add together. What if the En’s across all the resistors added up tosomething more or less than the supply voltage, E? Then there would have to be a“phantom EMF” some place, adding or taking away voltage. But there is no such.An EMF cannot come out of nowhere. This principle will be formalized later in thischapter.Look at this another way. The voltmeter V in Fig. 5-2 shows the voltage Eof the battery, because the meter is hooked up across the battery. The meter Valso shows the sum of the En’s across the set of resistors, because it’s con-nected across the set of resistors. The meter says the same thing whether youthink of it as measuring the battery voltage E, or as measuring the sum of theEn’s across the series combination of resistors. Therefore, E is equal to the sumof the En’s.This is a fundamental rule in series dc circuits. It also holds for 60-Hz utility ac cir-cuits almost all the time.5-1Light bulbs in series. An ammeter, A is placed in the circuit to measure current.