Capacitor C1 is initially charged to V1 and capacitor C2 is initially charged to V2. The capacitors are then connected to each other, positive terminal to positive terminal and negative terminal to negative terminal. If C1 = 24 μF with an initial voltage of 25 V, and capacitor C2 = 13 μF is charged to 11 V. What is the final voltage, in volts, across C1?

ΔV = 20.1 V

Explanation:

As the positive plates are connected to each other, the capacitors are connected in parallel, so the total system load is the sum of the charges on each capacitor.

               Q = Q₁ + Q₂

The charge on each capacitor is

            Q₁ = C₁ ΔV₁

            Q₁ = 24 10⁻⁶ 25

            Q₁ = 6.00 10⁻⁴ C

            Q₂ = C₂ ΔV₂

            Q₂ = 13 10⁻⁶ 11

            Q₂ = 1.43 10⁻⁴ C

The total set charge is

            Q = (6 + 1.43) 10⁻⁴

            Q = 7.43 10⁻⁴ C

The equivalent capacitance is

           C_eq = C₁ + C₂

           C_eq = (24 + 13) 10⁻⁶

           C_eq = 37 10⁻⁶ F

Let's use the relationship to find the voltage

          Q = C_eq ΔV

          ΔV = Q / C_eq

          ΔV = 7.43 10⁻⁴ / 37 10⁻⁶

          ΔV = 2.008 10¹

          ΔV = 20.1 V

This voltage is constant in the combination so it is also the voltage in capacitor C1

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