Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
In the circuit depicted in figure (a), the switch is closed at t = 0 and subsequently reopened after a long time at t = t₀ . Which of the following statements is correct regarding the circuit?
Options
- AThe charge on C a long time after t = t₀ is zero.
- BThe current through the resistor a long time after t = 0 (but before t = t₀ ) is E /R .
- CThe charge on C a long time after t = 0 (but before t = t₀ ) is E C .
- DThe charge on C immediately after t = 0 is E C .
Correct answer
C. The charge on C a long time after t = 0 (but before t = t₀ ) is E C .
Step-by-step solution
In the circuit shown in figure (a), when the switch is closed at t = 0 , the capacitor starts charging through the resistor. The charge on the capacitor as a function of time is given by q(t) = C E (1 - e^ -t/RC ) . Immediately after t = 0 , the charge on the capacitor is q(0) = 0 . A long time after t = 0 (but before t = t₀ ), the capacitor reaches its steady state and is fully charged. The charge on the capacitor becomes q = C E . In this steady state, the capacitor acts as an open circuit to direct current, so t