Question

Identify the valid statements relevant to the given circuit at the instant when the key is closed.
 

\( \text{A} \): There will be no current through resistor R.
\( \text{B} \): There will be maximum current in the connecting wires.
\( \text{C} \): Potential difference between the capacitor plates A and B is minimum.
\( \text{D} \): Charge on the capacitor plates is minimum.
Choose the correct answer from the options given below:

• A. C, D only
• B. B, C, D only
• C. A, C only
• D. A, B, D only

Hint:

At the instant a capacitor is connected in a circuit, it behaves like a short circuit because there is no initial charge, and the potential difference across it is zero.

Answer 1

The Correct Option is B

To solve this problem, let's analyze the circuit when the key is closed at the initial instant. 

1. Understanding the Circuit:
   • The circuit consists of a resistor \( R \), a capacitor with plates \( A \) and \( B \), a switch (key), and a 5V battery.
   • When the switch is closed, the capacitor will start charging from the battery.
2. Initial Instant Behavior:
   • At the very instant the switch is closed, the capacitor behaves like a short circuit because it is initially uncharged.
   • This means maximum current will flow through the wires as the capacitor starts to charge.
3. Analyzing each Statement:
   • Statement A: "There will be no current through resistor \( R \)" - This is incorrect. At the instant of closing the key, maximum current flows through the circuit as the capacitor starts charging.
   • Statement B: "There will be maximum current in the connecting wires" - This is correct. The initial surge current is the maximum as the capacitor charges from zero volts.
   • Statement C: "Potential difference between the capacitor plates A and B is minimum" - This is correct. Initially, the potential difference is zero as the capacitor is uncharged.
   • Statement D: "Charge on the capacitor plates is minimum" - This is correct. At the beginning, the charge on the capacitor is zero.
4. Conclusion:
   • The correct combination of statements is B, C, and D, indicating valid observations at the instant the key is closed.

Answer 2

The circuit in question involves a capacitor and resistors. Understanding the behavior of the circuit when the key is closed is essential in determining the validity of the given statements:

1. At the instant the key is closed, the capacitor initially behaves like a short circuit because it starts charging from 0 volts. Therefore, Statement A that mentions no current through resistor R is incorrect because the connecting wires will conduct maximum current to charge the capacitor.
2. In this initial condition, current is maximized through the connecting wires as there is no voltage across the capacitor initially (it hasn't had time to charge yet), thus supporting Statement B.
3. Statement C is valid since the potential difference across the capacitor plates is zero at the moment the circuit is closed. The voltage gradually increases as the capacitor charges.
4. Initially, the charge on the capacitor is zero, thus validating Statement D. The charge increases as the capacitor gets charged over time.

Therefore, the correct answer is: B, C, D only