91Ó°ÊÓ

In the context of RL circuits, the potential difference refers to the voltage across the resistor. When a battery is connected to an RL circuit, it provides an initial voltage. Upon removal of the battery, the potential difference begins to decrease over time.
This reduction in the potential difference is due to the energy stored in the inductor, which attempts to keep the current flowing even after the power source is disconnected.
As a result, the voltage across the resistor decreases exponentially with time. This is crucial to understand because our goal here is to determine how quickly this potential difference drops to a certain percentage of its original value.
To sum up, the potential difference changes dynamically based on circuit conditions and time. Understanding this fluctuation is key in analyzing RL circuits.

Inductance in an RL circuit is a property of the coil or inductor, symbolized by the letter 'L'. It is measured in Henrys (H) and it reflects the ability of the circuit to store energy in a magnetic field.
Inductance causes a delay in the change of current, which essentially influences how the potential difference evolves over time when the circuit is opened.

• A higher inductance value means more energy storage capability, hence a slower decay of current.
• In our exercise, the inductance is given as 2.00 H, indicating that the inductor is quite capable of storing energy.

Understandably, inductance plays a significant role in how quickly the potential difference decays, as it opposes changes in the current within the circuit.

Resistance in an RL circuit is the opposition to the flow of current and is symbolized by 'R'. It is measured in Ohms (Ω). In our particular problem, the resistance is 3.00 Ω.
The resistor is pivotal because it determines how quickly the potential difference decreases after the battery is removed.
The interplay between resistance and inductance dictates the rate of decay of voltage in the circuit. Simply put:

• A higher resistance results in a faster decay of potential difference.
• A lower resistance leads to a slower decay.

Thus, in the decay formula, both resistance and inductance must be considered to evaluate the time required to reach a specified potential difference.

Exponential decay in an RL circuit describes how the potential difference decreases over time, following an exponential curve. This phenomenon is mathematically represented by the equation: \[V(t) = V_0 e^{-\frac{R}{L}t}\]
Here:

• \(V(t)\) is the voltage at a time \(t\).
• \(V_0\) is the initial voltage.
• \(R\) is the resistance.
• \(L\) is the inductance.

In our specific problem, the aim is to find out 't', where 90% of the voltage has decayed. We did this by transforming and solving the equation to isolate 't'.
Exponential decay happens because the current and potential difference decrease at a rate proportional to their current value, which is a hallmark of exponential functions. By understanding this decay, it is possible to predict how long it will take to reach a certain voltage level in an RL circuit.