A series circuit is formed when any number of resistors are connected end-to-end so that there is only one path for current to flow. The resistors can be actual resistors or other devices that have resistance. The following illustration shows four resistors connected end-to-end. There is one path of current flow from the negative terminal of the battery through R4, R3, R2, R1 returning to the positive terminal.
Formula for Series Resistance The values of resistance add in a series circuit. If a 4 ohms resistor is placed in series with a 6 ohms resistor, the total value will be 10 ohms. This is true when other types of resistive devices are placed in series. The mathematical formula for resistance in series is:
Rt = R1 + R2 + R3 + R4 + R5+ Rn...
In this example, the circuit includes five series resistors.
Current in a Series Circuit The equation for total resistance in a series circuit allows us to simplify a circuit. Using Ohm’s Law, the value of current can be calculated. Current is the same anywhere it is measured in a series circuit.
Voltage in a Series Circuit
Voltage can be measured across each of the resistors in a circuit. The voltage across a resistor is referred to as a voltage drop. A German physicist, Gustav Kirchhoff, formulated a law which states the sum of the voltage drops across the resistances of a closed circuit equals the total voltage applied to the circuit. In the following illustration, four equal value resistors of 1.5 ohms each have been placed in series with a 12 volt battery. Ohm’s Law can be applied to show that each resistor will “drop” an equal amount of voltage.
If voltage were measured across any single resistor, the meter would read three volts. If voltage were read across a combination of R3 and R4 the meter would read six volts. If voltage were read across a combination of R2, R3, and R4 the meter would read nine volts. If the voltage drops of all four resistors were added together the sum would be 12 volts, the original supply voltage of the battery.
Voltage Division in a Series Circuit
It is often desirable to use a voltage potential that is lower than the supply voltage. To do this, a voltage divider, similar to the one illustrated, can be used. The battery represents Ein which in this case is 50 volts. The desired voltage is represented by Eout, which mathematically works out to be 40 volts. To calculate this voltage, first solve for total resistance.
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