A capacitor of capacitance C charged by an amount Q is connected in parallel with an uncharged capacitor of capacitance 2C. The final charges on the capacitors are

Question

A capacitor of capacitance C charged by an amount Q is connected in parallel with an uncharged capacitor of capacitance 2C. The final charges on the capacitors are (A) (Q/3), (2Q/3) (B) (Q/2), (Q/2) (C) (Q/5), (4Q/5) (D) (Q/4), (3Q/4)

Tardigrade Admin · Accepted Answer

The two capacitors attain common potential

(V_{c})

given by the relation.

V_{c} = \frac{T o t a l c ha r g e}{T o t a l C a p a c i t an ce} = \frac{Q + 0}{C + 2 C} = \frac{Q}{3 C}

The final charges on two capacitors are

Q_{1} = C V_{c} = \frac{CQ}{3 C} = \frac{Q}{3} an d Q_{2} = 2 C V_{c} = \frac{2 Q}{3}

Q. A capacitor of capacitance C charged by an amount Q is connected in parallel with an uncharged capacitor of capacitance 2C. The final charges on the capacitors are

$\frac{Q}{3}, \frac{2 Q}{3}$

$\frac{Q}{2}, \frac{Q}{2}$

$\frac{Q}{5}, \frac{4 Q}{5}$

$\frac{Q}{4}, \frac{3 Q}{4}$

Q. A capacitor of capacitance C charged by an amount Q is connected in parallel with an uncharged capacitor of capacitance 2C. The final charges on the capacitors are

3Q​,32Q​

2Q​,2Q​

5Q​,54Q​

4Q​,43Q​

The two capacitors attain common potential (Vc​) given by the relation. Vc​=TotalCapacitanceTotalcharge​=C+2CQ+0​=3CQ​ The final charges on two capacitors are Q1​=CVc​=3CCQ​=3Q​andQ2​=2CVc​=32Q​

$\frac{Q}{3}, \frac{2 Q}{3}$

$\frac{Q}{2}, \frac{Q}{2}$

$\frac{Q}{5}, \frac{4 Q}{5}$

$\frac{Q}{4}, \frac{3 Q}{4}$