Three resistors,each of resistance 12ohm,are connected in parallel.what is the equivalent resistance?

To find the equivalent resistance of resistors connected in parallel, we can use a specific formula that simplifies the calculation. When resistors are connected in parallel, the total or equivalent resistance (R_eq) can be calculated using the formula:

Formula for Parallel Resistance

The formula for calculating the equivalent resistance of multiple resistors in parallel is:

1/R_eq = 1/R1 + 1/R2 + 1/R3 + ...

In this case, since all three resistors have the same resistance value of 12 ohms, we can simplify our calculations.

Step-by-Step Calculation

• Identify the resistance values: R1 = 12 ohms, R2 = 12 ohms, R3 = 12 ohms.
• Apply the formula:

1/R_eq = 1/12 + 1/12 + 1/12

This simplifies to:

1/R_eq = 3/12

Now, we can simplify further:

1/R_eq = 1/4

To find R_eq, we take the reciprocal:

R_eq = 4 ohms

Understanding the Result

The equivalent resistance of 4 ohms indicates that when these three 12-ohm resistors are connected in parallel, they behave as a single resistor with a resistance of 4 ohms. This lower resistance value is a characteristic of parallel circuits, where the total resistance decreases as more resistors are added.

Real-World Analogy

Think of it like a group of people working together to complete a task. If one person can do a job in 12 hours, three people working together can finish it much faster. Similarly, in a parallel circuit, the pathways for current flow increase, allowing more current to pass through, which effectively reduces the overall resistance.

In summary, the equivalent resistance of three 12-ohm resistors connected in parallel is 4 ohms, demonstrating how parallel connections can significantly lower resistance compared to individual resistors. If you have any further questions or need clarification on this topic, feel free to ask!