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 ____________.

Options

• `"Q"/3, (2"Q")/3`

• `"Q"/2, "Q"/2`

• `"Q"/5, (4"Q")/5`

• `"Q"/4, (3"Q")/4`

Answer 1

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 `"Q"/3, (2"Q")/3`.

Explanation:

The two capacitors attain common potential (V_C) given by the relation,

`"V"_"C" = "Total charge"/"Total capacitance" = "Q" + 0/("C" + 2"C") = "Q"/(3"C")`

The final charges on two capacitors are

`"Q"_1 = "CV"_"C" = "CQ"/(3"C") = "Q"/3  "and"  "Q"_2 = 2"CV"_"C" = (2"Q")/3`