Resistor 

A resistor is an electrical component that opposes or resists the flow of electric current in a circuit. A resistor is a passive, two-terminal device used for controlling the current, reducing voltage, and dissipating energy as heat. The unit of measurement is ohms (Ω).

1.0What is a Resistor? 

A resistor is a component that imparts resistance to the circuit, limiting the flow of electric current. The resistance property of the material depends on the length, cross-sectional area, and temperature of the conductor. Primarily, a resistor is there to control the current as well as prevent other elements from excess current. While drawing a circuit diagram it is necessary to use different symbols for each type of resistor accordingly.

2.0Types of Resistor 

Resistors are categorized based on material, construction, and application:

1. Fixed Resistors: These resistors have a fixed resistance value. Examples:

• Carbon Composition Resistor: Made of carbon powder and binder for general-purpose applications.
• Metal Oxide Resistor: Much more stable than carbon resistors, can withstand high temperatures.
• Wire-Wound Resistor: It consists of a thin wire wound over a ceramic core. It is used for high-power applications.

2. Variable Resistors: Resistance value can be changed. Examples:

• Potentiometer: Changes voltage in the circuit (volume control).
• Rheostat: Used in controlling current in a circuit; for example, in light dimmers.

3.0Resistors in Series and Parallel Combinations 

Resistors are the basic component of electric circuits that help resist the flow of electric current, hence controlling the amount of current that passes through the circuit. A resistor is used to limit or regulate the flow of current to prevent overload of the circuit. The resistance (R) produced by the resistor is calculated in ohm (Ω).

Resistors can be combined in two primary configurations: Series and Parallel. The total or equivalent resistance is a function of the configuration.

Resistors in Series

• The total resistance is the sum of individual resistances: R_eq = R₁ + R₂ + …..
• Current: The same current flows through all resistors.
• Voltage: The total voltage is the sum of the voltage drops across each resistor.

Resistors in Parallel

• The total resistance is given by:$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+...$
• Current: The total current is the sum of the currents through each resistor.
• Voltage: The same voltage is applied to all resistors.

4.0Colour Coding of Carbon Resistor 

Resistors, especially carbon resistors, have colour bands that represent their resistance value and tolerance. The colour code has 4 or 5 bands:

• First Band: First digit of the resistance.
• Second Band: Second digit of resistance.
• Third Band: Multiplier (power of 10).
• Fourth Band: Tolerance (accuracy of the resistor).

Colour Code Chart

5.0Power Dissipation in a Resistor 

When current flows through a resistor, its energy is dissipated as heat. Power dissipation in a resistor is justified by the power theorem of a resistor. 

The Power theorem states that the power dissipated in a resistor is proportional to the square of the current flowing through it, the square of the voltage across it, and its resistance. Mathematically, the theorem is expressed as:

$P=I^{2}R$ or $P=\frac{V^2}{R}$

Here, 

• P = Power dissipated (in watts)
• I = Current through the resistor (in amperes)
• V = Voltage across the resistor (in volts)
• R = Resistance of the resistor (in ohms)

Note that a resistor must be chosen with the correct power rating to avoid damage to the circuit or overheating.

6.0Solved Examples

Problem 1: In the given circuit, there are five resistors with the following values:

• R1=10 Ω
• R2=20 Ω
• R3=30 Ω
• R4=40 Ω
• R5=50 Ω

The resistors are connected as follows:

1. R1 and R2​ are connected in series.
2. The combination of R1​ and R2 is connected in parallel with R3​.
3. The resulting combination is connected in series with R4​.
4. The final combination is connected in parallel with R5​.

If a potential difference of V=120 V is applied across the whole network, calculate the total resistance of the circuit.

Solution: Let's start with the series combination of Resistors (R1 and R2)

R_series = R1 + R2 

R_series = 10+20 = 30Ω

Combine R_series with R3 in parallel according to the question: 

$\frac{1}{R_{Parallel}}=\frac{1}{R_{series}}+\frac{1}{R3}$

$\frac{1}{R_{Parallel}}=\frac{1}{30}+\frac{1}{30}=\frac{2}{30}$

$\frac{1}{R_{Parallel}}=\frac{1}{15}$ Ω

$\frac{1}{R_{Parallel}}$= 15 Ω

Combine

$R_{Parallel}$ with R4 in series 

$R_{total1}=R_{Parallel}+R4=15+40=55$Ω

Now, combine R_{total 1} with R5 in parallel 

$\frac{1}{R_{total}}=\frac{1}{R_{total1}}+\frac{1}{R5}$

$\frac{1}{R_{total}}=\frac{1}{55}+\frac{1}{50}=\frac{50+55}{55\times 50}=\frac{105}{2750}$

$R_{total}=\frac{2750}{105}\approx 26.19\Omega$

Problem 2: A six-band resistor has the following colour bands: Blue, Grey, Black, Brown, Blue, and Silver. What is the resistance of this resistor?

Solution: For solving a six-band colour code, these are the points to remember: 

• The first four bands are representative of significant digits. 
• The fifth band is the multiplier. 
• The sixth band shows tolerance. 

Identifying the colour bands associated with each colour: 

Blue: 6, Grey: 8, Black: 0, Brown: 1 

Multiplier of Blue: 10⁶

Tolerance of silver: $\pm 10$%

The first four digits here are 6801. (according to the significant numbers) 

Thus, the resistance is: 

R = $6801\times 10^6=6.801\times 10^9\Omega$

So, the resistance of the resistor is $6.801\times 10^9\Omega$ with a tolerance of $\pm$10%.

Problem 3: A circuit with a potential difference of 120V consists of a 12 Ω resistor (R1​) and a 6 Ω resistor (R2​) are connected in series. The series combination of R1​ and R2​ is connected in parallel with a 10 Ω resistor (R3​). Calculate the total power dissipated in the entire circuit.

Solution: The total resistance of the Circuit = R_total

Resistance in series of R1 and R2 

R_series = R1+R2 = 12+6 = 18Ω

Resistance in parallel combination: 

$\frac{1}{R_{total}}=\frac{1}{R_{series}}+\frac{1}{R3}$

$\frac{1}{R_{total}}=\frac{1}{18}+\frac{1}{10}=\frac{5+9}{90}=\frac{14}{90}$

$R_{total}=\frac{90}{14}\approx 6.43$Ω

The power dissipated = P

$P=\frac{V^2}{R}$

$P=\frac{120\times 120}{6.43}=2239.50W$

7.0Applications of Resistors

• Current Limiting: Resistors limit the current that flows into components to prevent damage.
• Voltage Division: In voltage divider circuits, resistances divide down the voltage to a level that is desired.
• Heating Elements: In appliances such as electric heaters, resistors convert electrical energy into heat.
• Signal Processing: Resistors set gain and filter signals in amplifiers and other circuits.