Case study: A circuit consisting of a capacitor C, a resistor of resistance R and an ideal battery of emf V, as shown in figure is known as RC series circuit. As soon as the circuit is completed by closing key S1 (keeping S2 open) charges begin to flow between the capacitor plates and the battery terminals. The charge on the capacitor increases and consequently the potential difference Vc (=q/C) across the capacitor also increases with time. When this potential difference equals the potential difference across the battery, the capacitor is fully charged (Q=VC). During this process of charging, the charge q on the capacitor changes with time t as q=Q[1−e−t/RC]. The charging current can be obtained by differentiating it and using dxd(emx)=memx. Consider the case when R=20 kΩ, C=500μF and V=10 V.
a. (i) The final charge on the capacitor, when key S1 is closed and S2 is open, is
(A) 5μC (B) 5 mC (C) 25 mC (D) 0.1 C
b. (ii) For sufficient time the key S1 is closed and S2 is open. Now key S2 is closed and S1 is open. What is the final charge on the capacitor ?
(A) Zero (B) 5 mC (C) 2.5 mC (D) 5μC
c. (iii) The dimensional formula for RC is
(A) [M L2T−3A−2] (B) [M0L0T−1A0] (C) [M−1L−2T4A2] (D) [M0L0TA0]
d. (iv) The key S1 is closed and S2 is open. The value of current in the resistor after 5 seconds, is
(A) 2e1 mA (B) e mA (C) e1 mA (D) 2e1 mA
OR
(iv) The key S1 is closed and S2 is open. The initial value of charging current in the resistor, is
(A) 5 mA (B) 0.5 mA (C) 2 mA (D) 1 mA