To determine the type of circuit element placed in the closed box, we need to analyze the behavior of the potential difference across the box when a constant current is applied. Given that a constant current generator supplies 1 A at time t=0, we can infer how the potential difference changes over time based on the characteristics of different circuit elements.
Understanding Circuit Elements
In electrical circuits, different components respond uniquely to changes in current. Let's briefly review the four options provided:
- Resistance (2 ohm): A resistor would produce a constant voltage drop according to Ohm's Law (V = I × R). If we had a 2-ohm resistor with a constant current of 1 A, the voltage would be constant at 2 V.
- Battery (6 V): A battery maintains a constant voltage regardless of the current flowing through it, so the potential difference would remain at 6 V.
- Inductance (2 H): An inductor opposes changes in current. When a constant current is applied, the voltage across an inductor initially spikes but then stabilizes, depending on the rate of change of current.
- Capacitance (0.5 F): A capacitor stores charge and its voltage changes over time as it charges or discharges. When a constant current is applied, the voltage across a capacitor increases linearly over time (V = I × t / C).
Analyzing the Potential Difference
Since the problem states that the potential difference across the box varies according to a specific graph, we need to consider how each component behaves under a constant current. The key point here is that the voltage across a capacitor increases linearly when a constant current is applied. This means that if the graph shows a linear increase in voltage over time, it indicates the presence of a capacitor.
Mathematical Representation
For a capacitor, the relationship can be expressed as:
V(t) = (I × t) / C
In this case, with a current (I) of 1 A and a capacitance (C) of 0.5 F, the voltage across the capacitor at time t would be:
V(t) = (1 A × t) / 0.5 F = 2t
This indicates that the voltage increases linearly with time, which aligns perfectly with the behavior of a capacitor when subjected to a constant current.
Conclusion
Given the information and the behavior of the potential difference, the element in the box is indeed a capacitor with a capacitance of 0.5 F. This matches the answer choice (d) and explains why the voltage varies in a linear fashion when a constant current is applied. Understanding these fundamental principles helps in identifying circuit components based on their electrical characteristics.
