RESISTANCE IN PARALLEL
Parallel Connection of Three Resistors (10kΩ, 2kΩ, and 1kΩ) to a 9V Battery
Introduction:
In this write-up, we will explore the parallel connection of three resistors with different values—10kΩ, 2kΩ, and 1kΩ—powered by a 9V battery. We will discuss the characteristics of parallel circuits, the behavior of resistors in parallel, and calculate the total resistance and current in this configuration.
Parallel Circuit Overview:
In a parallel circuit, components are connected side by side, providing multiple paths for current flow. When resistors are connected in parallel, the voltage across each resistor is the same, and the total current flowing into the parallel combination is divided among the resistors.
Characteristics of Parallel Connection:
Voltage: In a parallel connection, each resistor experiences the same voltage. Therefore, in this circuit, each resistor will have a voltage of 9V across it.
Current: The total current flowing into the parallel combination is divided among the resistors based on their individual resistance values. The sum of the currents through each resistor equals the total current flowing into the parallel connection.
Calculating Total Resistance:
To determine the total resistance (Rt) of resistors connected in parallel, we can use the following formula:
1/Rt = 1/R1 + 1/R2 + 1/R3 + ...
In our case, the total resistance (Rt) can be calculated as:
1/Rt = 1/10kΩ + 1/2kΩ + 1/1kΩ
1/Rt = 0.0001 + 0.0005 + 0.001
1/Rt = 0.0016
Rt = 1/0.0016
Rt = 625Ω
The total resistance of the three resistors connected in parallel is 625Ω.
Calculating Total Current:
Since the total voltage across the parallel combination is 9V, we can calculate the total current (It) using Ohm's Law:
It = Vt / Rt
It = 9V / 625Ω
It = 0.0144A (or 14.4mA)
The total current flowing into the parallel connection is 14.4mA.
Conclusion:
In the given parallel circuit configuration, three resistors with values of 10kΩ, 2kΩ, and 1kΩ are connected in parallel to a 9V battery. Each resistor experiences the same voltage of 9V, and the total current flowing into the parallel combination is divided among the resistors based on their individual resistance values. The total resistance of the parallel combination is 625Ω, and the total current flowing into the circuit is 14.4mA.
Understanding the behavior of resistors in parallel is important in analyzing and designing electronic circuits, as it allows for the precise control and distribution of current. By applying the principles of parallel connections, engineers and enthusiasts can create circuits tailored to specific requirements and achieve desired outcomes.
