Concepts Of Physics MCQ Edition [Volume 2]
- Exam
- Concepts Of Physics MCQ Edition [Volume 2]
- Subject
- Physics
- Chapter
- Electric Current in Conductors
Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Current in Conductors
In a capacitor-charging circuit, let Q_1 denote the charge...
In a capacitor-charging circuit, let denote the charge delivered to the capacitor during an initial time interval of , and let denote the charge delivered during the subsequent interval. Additionally, assume that an initial of charge is deposited over a time interval , while the next of charge is deposited over the following time interval .
Options
- A,
- B,
- C,
- D,
Correct answer
D. ,
Step-by-step solution
The charge on a capacitor during charging is given by .
The charging current is the rate of flow of charge, given by .
Since the current decreases exponentially with time, the rate at which charge is delivered to the capacitor continuously decreases.
For a fixed time interval, the charge delivered is the area under the curve. Because is a decreasing function, the charge delivered in the first interval is greater than the charge delivered in the subsequent interval. Thus, .
Similarly, to deposit a fixed amount of charge (), it takes less time initially when the current is high, and more time later when the current is lower. Therefore, the time required to deposit the first is less than the time required to deposit the next . Thus, .
The charging current is the rate of flow of charge, given by .
Since the current decreases exponentially with time, the rate at which charge is delivered to the capacitor continuously decreases.
For a fixed time interval, the charge delivered is the area under the curve. Because is a decreasing function, the charge delivered in the first interval is greater than the charge delivered in the subsequent interval. Thus, .
Similarly, to deposit a fixed amount of charge (), it takes less time initially when the current is high, and more time later when the current is lower. Therefore, the time required to deposit the first is less than the time required to deposit the next . Thus, .