Introduction: Resistors connected to DC voltage sources play a crucial role in electronic circuits, allowing for voltage control, current limitation, and power dissipation. Understanding how resistors interact with DC sources is essential for circuit design and analysis. In this blog post, we will explore resistor connections to DC sources, discuss voltage division, power dissipation, and provide practical examples to enhance your understanding.
- Voltage
Division with Resistors: When a resistor is connected to a DC voltage
source in a series circuit, voltage division occurs. The voltage across
the resistor is determined by its resistance relative to the total
resistance in the circuit.
- Voltage
Division Formula: The voltage across a resistor (Vᵣ) in a series circuit
connected to a DC source can be calculated using the voltage division
formula:
Vᵣ = (Rᵣ / Rₜₒₜₐₗ) * Vₜₒₜₐₗ
Where: Vᵣ is the voltage across the resistor, Rᵣ is the
resistance of the resistor, Rₜₒₜₐₗ is the total resistance in the circuit, Vₜₒₜₐₗ is the total voltage supplied by
the DC source.
- Power
Dissipation in Resistors: When a resistor is connected to a DC source,
power is dissipated in the form of heat. The power dissipated by a resistor
can be calculated using Ohm's Law or the power formula:
P = (Vᵣ)² / Rᵣ
Where: P is the power dissipated by the resistor, Vᵣ is the
voltage across the resistor, Rᵣ is the resistance of the resistor.
- Practical
Examples: Let's consider a few practical examples to illustrate resistor
connections to DC sources:
Example 1: A 10 Ω resistor is connected in series with a 12
V DC source. The total resistance in the circuit is 30 Ω.
Using the voltage division formula: Vᵣ = (10 Ω / 30 Ω) * 12
V Vᵣ = (1/3) * 12 V Vᵣ = 4 V
Using the power dissipation formula: P = (4 V)² / 10 Ω P =
16 W / 10 Ω P = 1.6 W
Example 2: A circuit consists of two resistors in series, R₁
= 100 Ω and R₂ = 200 Ω, connected to a 9 V DC source.
Using the voltage division formula: Vᵣ₁ = (100 Ω / 300 Ω) *
9 V Vᵣ₁ = (1/3) * 9 V Vᵣ₁ = 3 V
Vᵣ₂ = (200 Ω / 300 Ω) * 9 V Vᵣ₂ = (2/3) * 9 V Vᵣ₂ = 6 V
Using the power dissipation formula: P₁ = (3 V)² / 100 Ω P₁
= 9 W / 100 Ω P₁ = 0.09 W
P₂ = (6 V)² / 200 Ω
P₂ = 36 W / 200 Ω P₂ = 0.18 W
Conclusion: Resistor connections to DC sources are
fundamental in electronic circuits, allowing for voltage division and power
dissipation. By understanding voltage division using the appropriate formula
and calculating power dissipation, you can effectively analyze and design
circuits involving resistors connected to DC sources. Consider the practical
examples provided to solidify your understanding and apply these concepts in
your circuit designs.