## Series Circuits

Topics Covered in this PPT

Why *I *Is the Same in All Parts of a Series Circuit

Total *R* Equals the Sum of All Series Resistances

Series* IR* Voltage Drops

Kirchhoff’s Voltage Law (KVL)

Polarity of *IR *Voltage Drops

Total Power in a Series Circuit

Series-Aiding and Series-Opposing Voltages

Analyzing Series Circuits with Random Unknowns

Ground Connections in Electrical and Electronic Systems

Troubleshooting: Opens and Shorts in Series Circuits

### Why I* *Is the Same in All Parts of a Series Circuit

**Characteristics of a Series Circuit**

- The current is the same everywhere in a series circuit.
- The total resistance is equal to the sum of the individual resistance values.
- The total voltage is equal to the sum of the
*IR* voltage drops across the individual resistances.
- The total power is equal to the sum of the power dissipated by each resistance.
- Current is the movement of electric charge between two points, produced by the applied voltage.
- The free electrons moving away from one point are continuously replaced by free electrons flowing from an adjacent point in the series circuit.
- All electrons have the same speed as those leaving the voltage source.
- Therefore,
*I *is the same in all parts of a series circuit.

Fig. 4-2: There is only one current in *R**1**, R**2*, and *R**3* in series. (*a*) Electron drift is the same in all parts of a series circuit. (*b*) Current *I* is the same at all points in a series circuit.

- Series Current Formulas
- Total current is the same as the individual currents in the series string:
*I**T **= I**1** = I**2** = I**3* = … = etc.

- Total current is equal to total voltage divided by total resistance:
- IT=VT/RT

- When a series circuit is connected to a voltage source, the free electrons must drift through all the series resistances.
- There is only one path for free electrons to follow.
- If there are two or more resistances in the same current path, the total resistance across the voltage source is the sum of all the resistances.

### Total *R* Equals the Sum of All Series Resistances

- Series Resistance Formulas
- The total resistance is the sum of the individual resistances.
*R**T** = R**1** + R**2** + R**3** + R**4** + R**5*
- Series Resistance Formulas
- Total resistance is equal to total voltage divided by the circuit current:
- Rt=Vt/It

### Series* IR* Voltage Drops

- By Ohm’s Law, the voltage across a resistance equals
*I **×** R.*
- In a series circuit, the
*IR* voltage across each resistance is called an *IR*** drop** or **voltage drop**, because it reduces the potential difference available for the remaining resistance in the circuit.

### Kirchhoff’s Voltage Law (KVL)

The *IR* drops must add to equal the applied voltage (KVL).

*V**T** = V**1** + V**2** + V**3** + V**4** + V**5*

*V**T** = IR**1** + IR**2** + IR**3** + IR**4 **+ IR**5*

*V**T* = 0.1 × 10 + 0.1 × 15 + 0.1 × 20 + 0.1 × 30 + 0.1 × 25

*V**T* = 1 V + 1.5 V + 2 V + 3 V + 2.5 V = 10 V

### Polarity of *IR *Voltage Drops

When current flows through a resistor, a voltage equal to *IR *is dropped across the resistor. The polarity of this *IR* voltage drop is:

__Negative__ at the end where the electrons enter the resistor.
__Positive__ at the end where the electrons leave the resistor.
- The rule is reversed when considering conventional current: positive charges move into the positive side of the
*IR* voltage.
- The polarity of the
*IR *drop is the same, regardless of whether we consider electron flow or conventional current.

### Total Power in a Series Circuit

- The power needed to produce current in each series resistor is used up in the form of heat.
- The total power used in the circuit is equal to the sum of the individual powers dissipated in each part of the circuit.
- Total power can also be calculated as
*V**T* *× **I*

**Finding Total Power**

*P**T** = P**1** + P**2** + P**3** + P**4** + P**5*

*P**T** = I**2**R**1** + I**2**R**2** + I**2**R**3** + I**2**R**4** + I**2**R**5*

*P**T* = 0.1 W + 0.15 W + 0.2 W + 0.3 W + 0.25 W = 1 W

*P**T* = 0.1 W + 0.15 W + 0.2 W + 0.3 W + 0.25 W = 1 W

### Series-Aiding and Series-Opposing Voltages

- Series-aiding voltages are connected with polarities that allow current in the same direction:
- The positive terminal of one is connected to the negative terminal of the next.
- They can be added to the total voltage.
- Series-opposing voltages are the opposite: They are connected to produce opposing directions of current flow.
- The positive terminal of one is connected to the positive terminal of another.
- To obtain the total voltage, subtract the smaller voltage from the larger.
- Two equal series-opposing voltage sources have a net voltage of zero.

### Analyzing Series Circuits with Random Unknowns

- When trying to analyze a series circuit, keep the following principles in mind:

**1.If ***I* is** known for one component, use this value in all components. **

- The current is the same in all parts of a series circuit.

**2.If ***I* is** unknown, it may be calculated in one of two ways:**

- Divide
*V**T* by *R**T*
- Divide an individual
*IR* drop by its *R*.
- Remember not to mix a total value for an entire circuit with an individual value for part of the circuit.

**3.If all individual voltage drops are known, add them to determine the applied ***V**T**.*

- A known voltage drop may be subtracted from
*V**T* to find a remaining voltage drop.

**Ground Connections in Electrical and Electronic Systems**

- In most electrical and electronic systems, one side of the voltage source is connected to ground.
- The reason for doing this is to reduce the possibility of electric shock.
- Figure 4-16 shows several schematic ground symbols:

- The ground is assumed to have a potential of 0 V regardless of the schematic symbol shown.
- These symbols are sometimes used inconsistently with their definitions. However, these symbols always represent a common return path for current in a given circuit.
- Voltages Measured with Respect to Ground
- When a circuit has a ground as a common return, measure the voltages with respect to this ground.

**Troubleshooting: Opens and Shorts in Series Circuits**

**The Effect of an Open in a Series Circuit**

- An open circuit is a circuit with a break in the current path. When a series circuit is open, the current is zero in all parts of the circuit.
- The total resistance of an open circuit is infinite ohms.
- When a series circuit is open, the applied voltage appears across the open points.
- Applied voltage
*V**T* is still present, even with zero current.
- The voltage source still has its same potential difference across its positive and negative terminals.
- Example: The 120-V potential difference is always available from the terminals of a wall outlet.
- If an appliance is connected, current will flow.
- If you touch the metal terminals when nothing else is connected, you will receive a shock.

**The Effect of a Short in a Series Circuit**

- When part of a series circuit is shorted, the current flow increases.
- When part of a series circuit is shorted, the voltage drops across the non-shorted elements increase.
- The voltage drop across the shorted component drops to 0 V.
- When troubleshooting a series circuit containing three or more resistors, remember:
- The component whose voltage changes in the opposite direction of the other components is the defective component.