question_answer

Directions: In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:

Capacitor\[{{C}_{1}}\]of capacitance\[1\,\mu F\]and capacitor\[{{C}_{2}}\] of capacitance 2uF are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time\[t=0\]. (1) The currents in the two discharging circuits at\[t=0\]are equal but not zero (2) The current in each of the two discharging circuits is zero at\[t=0\] (3) The current in the two discharging circuits at\[t=0\]are unequal (4) Capacitor\[{{C}_{1}}\]losses 50% of its initial charge sooner than\[{{C}_{2}}\]losses 50% of its initial charge

A)  1 and 2 are correct

B)  2 and 3 are correct

C)  1 and 4 and correct

D)  1, 2 and 4 are correct

Correct Answer: C

Solution :

                 The discharging current in the circuit is , \[i={{i}_{0}}{{e}^{-t/CR}}\] Here, \[{{i}_{0}}=\]initial current \[=\frac{V}{R}\] Here, V is the potential with which capacitor was charged. Since, V and R for both the capacitors are same, initial discharging current will be same but non-zero. Further \[\tau =CR\]                 \[{{C}_{1}}<{{C}_{2}}\] or            \[{{\tau }_{{{C}_{1}}}}<{{\tau }_{{{C}_{2}}}}\] or\[{{C}_{1}}\]loses its 50% of initial charge sooner than \[{{C}_{2}}\].