Resistors in Series and Parallel: Formulas, Diagrams & FAQs
A resistor is a fundamental passive electrical component found in nearly every electronic and electrical circuit. Its main purpose is to create resistance to the flow of electric current, allowing designers to control, limit, or divide electrical current and voltage in circuits. Resistance is measured in ohms (Ω). One ohm is defined as the resistance that allows one ampere (A) of current to flow with a voltage drop of one volt (V) across the terminals.
The relationship between voltage (V), current (I), and resistance (R) is expressed by Ohm’s law:
Resistor Definition and Symbol
A resistor is a two-terminal device that passively resists or limits the flow of electrons, regulating current in circuits. Standard circuit diagrams illustrate a resistor with either a zigzag (ANSI) or rectangular (IEC) symbol. The value and properties of a resistor are crucial for safe and functional circuit operation.
Resistors help achieve critical tasks such as current limitation, voltage division, energy dissipation as heat, and setting circuit gains and time constants. Their sizes and resistance values vary widely, from very small chips in integrated circuits to large devices used in industrial power applications.
Types of Resistors and Materials
Resistors can be classified based on their function or the materials used in their construction. Understanding the type is important for selecting the right component in a given application.
| Type | Description | Example |
|---|---|---|
| Fixed Resistor | Resistance value is set during manufacturing | Carbon composition, metal film |
| Variable Resistor | Adjustable resistance | Potentiometer, rheostat |
| Special Functional Resistor | Resistance varies with physical quantity | Thermistor (temperature), photoresistor (light) |
Common material-based resistor types include carbon film (moderate accuracy), metal film and metal oxide film (used for stable, precise values), wirewound (high precision, high power), and foil resistors (very high stability and low noise). The construction impacts their precision, tolerance, temperature behavior, and cost.
Resistor Characteristics
Key parameters of a resistor include its resistance value (in ohms), manufacturing tolerance (as a percentage of value), stability, temperature coefficient, and power rating. Power rating indicates the maximum power a resistor can safely dissipate. Precision applications need low noise and stable resistance across temperature changes.
For more on related concepts, see
Carbon Resistor and
Electrical Resistance.
Resistor Color Code
Fixed resistors are commonly labeled with colored bands to indicate their resistance value and tolerance. This color code allows quick identification, especially where printing numbers is difficult. Each band’s color represents a digit, a multiplier, or the tolerance.
| Color | Digit | Multiplier | Tolerance (%) |
|---|---|---|---|
| Black | 0 | 1 | – |
| Brown | 1 | 10 | ±1 |
| Red | 2 | 100 | ±2 |
| Orange | 3 | 1k | – |
| Yellow | 4 | 10k | – |
| Green | 5 | 100k | ±0.5 |
| Blue | 6 | 1M | ±0.25 |
| Violet | 7 | 10M | ±0.1 |
| Gray | 8 | 100M | – |
| White | 9 | 1G | – |
| Gold | – | 0.1 | ±5 |
| Silver | – | 0.01 | ±10 |
| None | – | – | ±20 |
Explore detailed explanations with Resistor Colour Codes.
Resistors in Series and Parallel
In circuit design, resistors are often connected in series or parallel for desired total resistance. For resistors in series, the equivalent resistance is the sum of individual resistances. For resistors in parallel, the reciprocal of the equivalent resistance is the sum of reciprocals of each.
| Arrangement | Formula | Application |
|---|---|---|
| Series | Req = R1 + R2 + ... + Rn | Increase total resistance; current same through all |
| Parallel | 1/Req = 1/R1 + 1/R2 + ... + 1/Rn | Decrease total resistance; voltage same across all |
To explore circuit combinations, see Resistors in Series and Parallel.
Stepwise Approach to Solving Resistor Problems
- Read the circuit and identify arrangement: series, parallel, or mixed.
- Write the matching formula for the circuit type.
- Substitute given resistor values into the formula.
- Calculate total or unknown resistance, or solve for current/voltage as required.
- Check units and review answer for logic.
Brush up on related techniques using Ohm's Law and Difference Between Resistance and Resistivity.
Key Example Problems
Example 1: Three resistors (2 Ω, 3 Ω, 5 Ω) are connected in series.
Total resistance = 2 + 3 + 5 = 10 Ω.
Example 2: If three resistors (4 Ω, 6 Ω, 12 Ω) are connected in parallel:
1/Req = 1/4 + 1/6 + 1/12 = (3+2+1)/12 = 6/12 = 1/2
So, Req = 2 Ω.
Common Applications of Resistors
- Current limiting for LEDs and devices
- Voltage dividing to provide stable voltages at different points
- Setting time constants in combination with capacitors
- Shunt resistors for current measurement
- Gain control in amplifiers
Special resistors are used in automotive, lighting, measurement, and signal processing applications. For more, check Uses of Resistor.
Comparison: Resistance vs. Resistivity
| Parameter | Resistance | Resistivity |
|---|---|---|
| Definition | Property of a component to oppose current flow | Intrinsic property of the material itself |
| Formula | R = ρ (l/A) | ρ = RA / l |
| Unit | Ohm (Ω) | Ohm-meter (Ω·m) |
| Depends On | Material, length, area | Material only |
To understand this difference, refer to Difference Between Resistance and Resistivity.
Further Learning and Practice
- Revise NCERT Physics chapters on Current Electricity and Electric Current in Conductors.
- Practice resistor network questions using sample problems from Resistor Combinations.
- Test your understanding with Ohm’s Law and Resistance worksheets.
- Explore more about unit and measurement with Unit of Resistance.
Mastering resistor concepts is essential for building comfort with more complex topics in Physics and circuit analysis. Continue practicing with internal resources to deepen your understanding.
FAQs on Resistor Explained: Working, Types, and Applications
1. What is a resistor?
A resistor is a passive electrical component that limits or regulates the flow of electric current in a circuit. Resistors are measured in ohms (Ω) and are essential for controlling voltage, current, and protecting sensitive electronic parts.
2. What is the SI unit of resistor?
The SI unit of resistance is the ohm (Ω). One ohm represents the resistance between two points if a 1-volt potential difference produces a 1-ampere current.
3. What is the function of a resistor in a circuit?
A resistor controls and limits the electric current flow within a circuit. Main functions include:
• Preventing excessive current
• Dividing voltage
• Protecting sensitive components
• Reducing signal levels and generating heat where necessary
4. State the formula for resistance of a resistor.
The resistance (R) of a resistor is calculated by Ohm's Law:
R = V / I,
where V = voltage (volt), I = current (ampere), R = resistance (ohm).
5. What are the different types of resistors?
Common types of resistors include:
• Fixed Resistors (carbon composition, metal film, wire-wound)
• Variable Resistors (potentiometer, rheostat)
• Special Purpose (thermistors, photoresistors, varistors, strain gauges)
Each type is selected based on function, precision, and application requirements.
6. How do you calculate the total resistance of resistors connected in series and parallel?
For series: Rtotal = R1 + R2 + ... + Rn
For parallel: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn
Key point: Series combination increases resistance, while parallel combination decreases total resistance.
7. What is the color code of a resistor?
The resistor color code is a standardized marking using colored bands to indicate resistance value and tolerance. 4-band code:
• 1st & 2nd bands: significant digits
• 3rd band: multiplier
• 4th band: tolerance
Refer to the color chart for digit and multiplier meanings.
8. What is the difference between resistance and resistivity?
Resistance (R) is the opposition a conductor offers to current flow, measured in ohms (Ω). Resistivity (ρ) is a material property, indicating how strongly a material resists current, measured in ohm-meter (Ω·m). Resistivity is constant for a material; resistance depends on length, area, and resistivity.
9. How does temperature affect the resistance of a resistor?
For most conductors, resistance increases with temperature due to greater vibrational energy of atoms impeding electron flow.
• Metals: Higher temperature = higher resistance
• Semiconductors/NTC thermistors: Resistance decreases with increasing temperature
10. How do you read the value of a surface mount (SMD) resistor?
SMD resistors use a numerical code:
• The first two digits indicate significant figures.
• The third digit is the multiplier (number of zeros to add).
Example: '472' means 47 × 102 = 4700 Ω = 4.7 kΩ.
11. What are common applications of resistors?
Resistors are widely used for:
• Current limiting (e.g., with LEDs)
• Voltage division
• Biasing active devices (transistors)
• Protection of components
• Signal conditioning and filtering circuits
12. Explain the difference between a fixed resistor and a variable resistor.
A fixed resistor has a set resistance value that cannot be changed, while a variable resistor can be adjusted to change its resistance, allowing control of current or voltage. Examples: Fixed (carbon film), Variable (potentiometer, rheostat).
