What is the equivalent resistance of a network having 5 resistors of each 10ohm connected in parallel? 

Explanation:

Equivalent Resistance of Resistors in Parallel

Definition: When resistors are connected in parallel, the total or equivalent resistance of the network is less than the smallest resistor in the parallel arrangement. The formula for calculating the equivalent resistance (R_eq) of resistors connected in parallel is:

Formula:

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

Here, R₁, R₂, R₃, ..., R_n are the individual resistances of the resistors in the parallel network.

Problem Analysis:

In this problem, we are given:

• 5 resistors, each with a resistance of 10 Ω.
• These resistors are connected in parallel.

Step-by-Step Calculation:

Step 1: Write the formula for equivalent resistance in parallel:

Step 2: Substitute the values of resistors:

Since all resistors have the same resistance (10 Ω), we can simplify the formula:

Step 3: Add the reciprocals:

Step 4: Simplify the fraction:

Step 5: Take the reciprocal to find R_eq:

Final Answer:

The equivalent resistance of the network is 2 Ω.

Advantages of Parallel Connection:

• In parallel circuits, the total resistance is reduced, which allows more current to flow through the circuit.
• If one resistor fails, the other resistors continue to function, ensuring that the circuit remains operational.

Correct Option: The correct answer is Option 4, which states that the equivalent resistance is 2 Ω.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 10 Ω

This option is incorrect because the equivalent resistance of resistors in parallel is always less than the smallest individual resistance in the network. Since all resistors have a resistance of 10 Ω, the equivalent resistance must be less than 10 Ω.

Option 2: 50 Ω

This option is incorrect because 50 Ω is the sum of the resistances if they were connected in series. In a parallel connection, the resistances combine differently, resulting in a much smaller equivalent resistance.

Option 3: 500 Ω

This option is incorrect as it is significantly larger than the resistance values of individual resistors. The equivalent resistance in parallel is always less than the smallest resistor in the network, and 500 Ω is not plausible in this case.

Option 4: 2 Ω

This is the correct answer, as calculated above.

Conclusion:

Understanding how resistors combine in parallel circuits is essential for analyzing electrical networks. In this problem, the resistors combine to produce an equivalent resistance of 2 Ω, which is less than the resistance of any individual resistor in the network. This reduction in resistance is a key characteristic of parallel circuits, making them beneficial in applications requiring lower resistance and higher current flow.