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Series Connection of Three Resistors (10kΩ, 2kΩ, and 1kΩ) to a 9V Battery
Introduction:
This write-up discusses the series connection of three resistors with different values—10kΩ, 2kΩ, and 1kΩ—powered by a 9V battery. We will explore the characteristics of series circuits, analyze the behavior of resistors in series, and calculate the total resistance and current in this configuration.
Series Circuit Overview:
In a series circuit, components are connected end-to-end, forming a single path for current flow. When resistors are connected in series, the same current passes through each resistor, and the total resistance of the series combination is the sum of the individual resistances.
Characteristics of Series Connection:
Current: In a series connection, the current remains constant throughout all the components. The same current flows through each resistor in the series.
Voltage: The total voltage across a series connection is the sum of the individual voltage drops across each resistor. The voltage drop across each resistor is proportional to its resistance value.
Calculating Total Resistance:
To determine the total resistance (Rt) of resistors connected in series, we simply add the individual resistance values:
Rt = R1 + R2 + R3
Rt = 10kΩ + 2kΩ + 1kΩ
Rt = 13kΩ
The total resistance of the three resistors connected in series is 13kΩ.
Calculating Total Current:
Using Ohm's Law, we can calculate the total current (It) flowing through the series circuit:
It = Vt / Rt
It = 9V / 13kΩ
It ≈ 0.6923mA (or 0.6923A)
The total current flowing through the series circuit is approximately 0.6923mA.
Voltage Drop across Each Resistor:
The voltage drop across each resistor can be calculated by multiplying its resistance with the total current:
V1 = R1 * It
V1 = 10kΩ * 0.6923mA
V1 ≈ 6.923V
V2 = R2 * It
V2 = 2kΩ * 0.6923mA
V2 ≈ 1.385V
V3 = R3 * It
V3 = 1kΩ * 0.6923mA
V3 ≈ 0.6923V
The voltage drop across the 10kΩ resistor is approximately 6.923V, across the 2kΩ resistor is approximately 1.385V, and across the 1kΩ resistor is approximately 0.6923V.
Conclusion:
In the given series circuit configuration, three resistors with values of 10kΩ, 2kΩ, and 1kΩ are connected in series to a 9V battery. The same current flows through each resistor, and the voltage drop across each resistor is proportional to its resistance value. The total resistance of the series combination is 13kΩ, and the total current flowing through the circuit is approximately 0.6923mA.
Understanding the behavior of resistors in series is crucial for analyzing and designing electronic circuits, enabling precise current control and voltage distribution. By applying the principles of series connections, engineers and enthusiasts can create circuits tailored to specific requirements and achieve desired outcomes.
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