Answer to Question #228636 in Electric Circuits for Nomo

Question

Consider two capacitors, one having a capacitance twice the other, in two separate electric circuits. The same potential difference is applied to it. The charge that can be accumulated on the armatures of the two Capacitors:

A.     Depends on the resistance of the circuit

B.     Is the same because it is independent of the capacitor

C.     Is equal to half at the level of the capacitor of double capacitance

D.     Is double at the level of the capacitor with double capacitance

 

Answer 1

Explanations & Calculations

• According to the equation $\small Q= CV_0 .\large e^{\frac{-t}{RC}}$ the charge accumulated on each capacitor depends on the circuit resistance. So Answer A is correct.
• Provided that the same resistance up to each capacitor & under that same voltage applies to each of them Answer C becomes true according to that equation as the exponential part becomes constant.

$\qquad\qquad \begin{aligned} \small Q&=\small CV_0.e^{\frac{-t}{k}}\to C.K........(K= constant)\\ \small Q_1&=\small CK........(1)\\ \small Q_2 &=\small 2CK........(2)\\\\ &\small (1)/(2),\\\\ \small Q_1&=\small \frac{Q_2}{2} \end{aligned}$

• Therefore, Answer A and C is the correct combination.