Question

A 12.0 µF сapacitor is charged to a potential difference of 150 V. The terminals of the charged capacitor are then connected to those of an uncharged 6.0 µF capacitor. Calculate final potential difference across and charge on, each capacitor.

Answer 1

Given: C₁ = 12µF

V₁ = 150 V

C₂ = 6µF

`Q_"initial"` = C₁V₁

= 12 × 150

= 1800 µC

Total charge is conserved.

After the connection, the capacitors are in parallel. Total capacitance:

C_eq = C₁ + C₂

= 12 + 6

= 18µF

Final voltage (V_f) = `Q_"total"/C_(eq)`

= `1800/18`

= 100 V

Final charge on 12 µF:

Q₁ = C₁V_f

= 12 × 100

= 1200 µC

Final charge on 6 µF:

Q₂ = C₂V_f

= 6 × 100

= 600 µC