An RL series circuit has R = 10 ohms and L = 0.1 H. The time constant of this circuit is:

Explanation:

Time Constant in an RL Circuit

Definition: The time constant (τ) of an RL (Resistor-Inductor) series circuit is a measure of the time it takes for the current to either reach approximately 63.2% of its final value after a change in voltage or to decay to about 36.8% of its initial value when the circuit is disconnected from the voltage source. It is a crucial parameter in analyzing the transient response of the circuit.

Formula: The time constant of an RL circuit is given by the formula: \[ \tau = \frac{L}{R} \] where: - \( \tau \) is the time constant in seconds, - \( L \) is the inductance in henries (H), - \( R \) is the resistance in ohms (Ω).

Given Data:

• Resistance, \( R = 10 \) ohms
• Inductance, \( L = 0.1 \) henries

Calculation:

Using the formula for the time constant: \[ \tau = \frac{L}{R} \] \[ \tau = \frac{0.1 \text{ H}}{10 \text{ Ω}} \] \[ \tau = 0.01 \text{ seconds} \] Since 1 second = 1000 milliseconds, \[ \tau = 0.01 \text{ seconds} \times 1000 \text{ milliseconds/second} \] \[ \tau = 10 \text{ milliseconds} \]

Therefore, the time constant of the RL circuit is 10 milliseconds.

Correct Option Analysis:

The correct option is:

Option 1: 10 milliseconds

This option correctly represents the calculated time constant of the given RL circuit with R = 10 ohms and L = 0.1 H.

Additional Information

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

Option 2: 100 milliseconds

This option is incorrect because the correct time constant calculated using the given values is 10 milliseconds, not 100 milliseconds. If the inductance or resistance values were different, the time constant might change accordingly, but with the given values, 100 milliseconds is not accurate.

Option 3: 100 seconds

This option is also incorrect. A time constant of 100 seconds implies an extremely high inductance or low resistance value, which is not the case with the given values of R and L. The calculation clearly shows the time constant to be in milliseconds, not seconds.

Option 4: 1 second

This option is incorrect as well. A time constant of 1 second would require a different set of values for inductance and resistance, specifically a much higher inductance or lower resistance than what is provided. The calculated value is 10 milliseconds, indicating a much shorter time constant.

Conclusion:

Understanding the concept of the time constant in an RL circuit is essential for analyzing its transient behavior. The time constant is determined by the ratio of the inductance to the resistance in the circuit. In this specific case, with R = 10 ohms and L = 0.1 H, the time constant is accurately calculated to be 10 milliseconds. This brief time constant indicates that the circuit responds relatively quickly to changes in voltage, reaching significant portions of its final value within a short period. Analyzing and comparing the given options highlights the importance of precise calculations and understanding the underlying principles of electrical circuits.