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QPages 197-198: Q9: HC Verma: Concepts of Physics - Volume 2 Electric Current in Conductors Pages 197-198: Q9 Solution: A capacitor of capacitance 1 _F and a capacitor of capacitance…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students often think a larger capacitor will discharge with a larger initial current because it stores more charge. In fact, the initial current is $I_0=V_0/R$, independent of $C$. The capacitance only affects the time constant $ au=RC$, not the starting current.
A capacitor of capacitance 1 _F and a capacitor of capacitance 2 _F are separately charged by a common battery for a long time. The two capacitors are then separately discharged through equal resistors. Both the discharge circuits are connected at t = 0.
Multiple Choice Options
- A a) The current in�C1_�discharge circuit is greater than that in�C2_�at�t=0,
- B b) The current in�C2_�discharge circuit is greater than that in�C1_�at�t=0,
- C c) The current in�C1_�discharge circuit is equal to that in�C2_�at�t=0,
- D d) The charge on�C1_decreases faster than that on�C2_
Step-by-Step Verified Solution
**Answer:** (b) C_ loses 50% of its initial charge sooner than C_ loses 50% of its initial charge.
**Step-by-Step Explanation:**
Time constant _ = RC. For C_ (1 _F) and C_ (2 _F), __ < __. So C_ loses charge faster.
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