Question

A network of resistances, cell and capacitor \( C = (2 + 4) \, \text{F} \) is shown in the adjoining figure. In steady state condition, the charge on \( 2 \, \text{F} \) capacitor is \( Q \), while \( R \) is unknown resistance. Values of \( Q \) and \( R \) are respectively

• A. \( 4 \, \mu \text{C} \) and \( 10 \, \Omega \)
• B. \( 4 \, \mu \text{C} \) and \( 4 \, \Omega \)
• C. \( 2 \, \mu \text{C} \) and \( 4 \, \Omega \)
• D. \( 2 \, \mu \text{C} \) and \( 8 \, \Omega \)

Hint:

In circuits with capacitors, the charge is directly proportional to the voltage and capacitance. The voltage is related to the current and resistance.

Answer 1

The Correct Option is A

Step 1: Charge and voltage relationship.
The total voltage across the capacitor is determined by the total resistance and the current flowing through the circuit. Using Ohm’s law and the capacitive relation \( Q = C V \), we can solve for \( Q \) and \( R \).

Step 2: Conclusion.
The values of \( Q \) and \( R \) are \( 4 \, \mu \text{C} \) and \( 10 \, \Omega \), respectively. This corresponds to option (1).