Series Circuit

Current in a Series Circuit

Since there is only one path for current in a series circuit, the same current must flow through each component of the circuit.

To determine the current in a series circuit, only the current through one of the components need be known. The fact that the same current flows through each component of a series circuit can be verified by inserting meters into the circuit at various points, as shown in the illustration below.

If this were done, each meter would be found to indicate the same value of current.

Current in a series circuit

Current in a series circuit.

Voltage in a Series Circuit

The voltage dropped across the resistor in a circuit consisting of a single resistor and a voltage source is the total voltage across the circuit and is equal to the applied voltage. The total voltage across a series circuit that consists of more than one resistor is also equal to the applied voltage, but consists of the sum of the individual resistor voltage drops.

In any series circuit, the SUM of the resistor voltage dropsmust equal the source voltage. This statement can be proven by an examination of the circuit shown in the following illustration below.

In this circuit a source potential (ET) of 20 volts is dropped across a series circuit consisting of two 5-ohm resistors. The total resistance of the circuit (RT) is equal to the sum of the two individual resistances, or 10 ohms. Using Ohm’s law the circuit current may be calculated as follows:

ohm's law circuit current formula

Calculating individual voltage drops in a series circuit

Since the value of the resistors is known to be 5 ohms each, and the current through the resistors is known to be 2 amperes, the voltage drops across the resistors can be calculated. The voltage (E1) across R1 is therefore:

calculating voltage drops on a dc series circuit formula

By inspecting the circuit, you can see that R2 is the same ohmic value as R1 and carries the same current. The voltage drop across R2 is therefore also equal to 10 volts. Adding these two 10-volts drops together gives a total drop of 20 volts, exactly equal to the applied voltage.

For a series circuit then:

ET = E1 = E 2 + E3 = . . . En

Example: A series circuit consists of three resistors having values of 20 ohms, 30 ohms, and 50 ohms, respectively. Find the applied voltage if the current through the 30 ohm resistor is 2 amps. (The abbreviation amp is commonly used for ampere.)

To solve the problem, a circuit diagram is first drawn and labeled like the illustration shown below.

Solving for applied voltage in a series circuit graphic

Solving for applied voltage in a series circuit formula

Solving for applied voltage in a series circuit substitution formula

NOTE: When you use Ohm’s law, the quantities for the equation MUST be taken from the SAME part of the circuit. In the above example the voltage across R2 was computed using the current through R2 and the resistance of R2.

The value of the voltage dropped by a resistor is determined by the applied voltage and is in proportion to the circuit resistances. The voltage drops that occur in a series circuit are in direct proportion to the resistances. This is the result of having the same current flow through each resistor—thelarger the ohmic value of the resistor, the larger the voltage drop across it.

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