10 resistance of one ohm each are connected in series and then connected to 10 V DC supply. If one of the resistance gets open, current in the circuit is:

Explanation:

Let's analyze the given problem in detail to understand why the correct answer is option 4.

We have 10 resistors, each with a resistance of 1 ohm, connected in series. When resistors are connected in series, their total or equivalent resistance (R_total) is the sum of their individual resistances. Therefore, the total resistance in this case is:

R_total = 1Ω + 1Ω + 1Ω + 1Ω + 1Ω + 1Ω + 1Ω + 1Ω + 1Ω + 1Ω

R_total = 10Ω

Next, this series combination is connected to a 10 V DC supply. The current (I) flowing through the circuit can be calculated using Ohm's Law, which states that:

V = I × R

Where:

• V is the voltage across the circuit (10 V)
• R is the total resistance (10 Ω)

Rearranging Ohm's Law to solve for the current (I) gives:

I = V / R

Substituting the given values:

I = 10 V / 10 Ω

I = 1 A

Therefore, if all resistors are intact, the current flowing through the circuit would be 1 A.

Now, let's consider the scenario where one of the resistors gets open. When a resistor in a series circuit opens, it effectively breaks the circuit. This means that there will be no closed path for the current to flow. In an open circuit, the current is zero because there is a break in the circuit that prevents the flow of electric charge.

Therefore, if one of the resistors in the series circuit gets open, the current in the circuit will be:

I = 0.0 A

Correct Option Analysis:

The correct option is:

Option 4: 0.0 A

This option correctly indicates that the current in the circuit will be zero if one of the resistors in the series circuit gets open.

Additional Information

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

Option 1: 1 A

This option would be correct if all the resistors were intact and the circuit was complete. As calculated earlier, the current in the circuit with all resistors intact is 1 A. However, this is not the case when one resistor is open.

Option 2: 10/9 A

This option is not correct in this context. The calculation seems to imply a scenario where the resistance is slightly less than the total resistance of 10 Ω, but it does not apply to the open circuit case.

Option 3: 0.1 A

This option is also incorrect. It might be a result of misunderstanding the problem or incorrect calculation. With one resistor open, the current cannot be 0.1 A because the circuit is broken, and no current can flow.

Conclusion:

Understanding the behavior of series circuits is essential for correctly identifying the effects of an open resistor. In a series circuit, the current is the same through all components, and if one component fails by becoming open, it disrupts the entire circuit, resulting in zero current flow. This fundamental principle is crucial for analyzing and troubleshooting series circuits in various applications.