Resistors in Parallel
In a parallel circuit, multiple resistors are connected across the same voltage source, meaning that they share the same potential difference (voltage). This configuration significantly affects the total current flowing through the circuit and the equivalent resistance.
Key Concepts
- Total Current: The total current (I) flowing through the parallel network is equal to the sum of the currents through each resistor:
$$I = I_1 + I_2 + I_3$$
Where \(I_1\), \(I_2\), and \(I_3\) are the currents through the individual resistors \(R_1\), \(R_2\), and \(R_3\) respectively.
- Equivalent Resistance: The equivalent resistance (\(R_p\)) of resistors in parallel can be found using the formula:
$$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$
This means that the equivalent resistance of a parallel circuit is less than any individual resistance within it. This characteristic allows more current to flow through the circuit compared to individual resistors alone.
Example Calculation
Consider three resistors with resistances 5 Ω, 10 Ω, and 30 Ω connected to a battery of 12 V. The voltage across each resistor is 12 V. The individual currents can be calculated using Ohm’s law:
- For \(R_1 = 5 Ω\): \(I_1 = \frac{12V}{5Ω} = 2.4 A\)
- For \(R_2 = 10 Ω\): \(I_2 = \frac{12V}{10Ω} = 1.2 A\)
- For \(R_3 = 30 Ω\): \(I_3 = \frac{12V}{30Ω} = 0.4 A\)
Total current flowing from the battery is:
$$I = I_1 + I_2 + I_3 = 2.4 A + 1.2 A + 0.4 A = 4 A$$
Understanding the concept of resistors in parallel is crucial for effectively designing electrical circuits, as it allows for the control of current flow and the flexibility to add or remove components without significantly affecting overall performance.