Combining Capacitors in Series & Parallel Practice Problems

While assembling an electric circuit, a student connects a network of three capacitors, C₁ = 10 pF, C₂ = 7 pF, and C₃ = 8 pF, as displayed in the figure. What is the equivalent capacitance (C_eq) between the two points, L and M?

In a laboratory experiment, you have a capacitor with a fixed capacitance of 40 nF and a variable capacitance that can be adjusted between 10 nF and 100 nF. Your task is to arrange the two capacitors in a circuit to obtain an equivalent capacitance of 24 nF. Determine how the two capacitors should be connected (in series or parallel) and what value the variable capacitance should be set to.

You have 50 identical capacitors, each with a capacitance of 1.0 μF. Determine the equivalent capacitance when all the capacitors are connected i) in series and ii) in parallel.

Determine the equivalent capacitance between points M and N of the arrangement of the capacitors shown in the figure below.

Work out the effective capacitance of the capacitors when connected, as shown below.

Consider a circuit where three capacitors (with capacitances of 5.0 μF, 7.0 μF, and 4.0 μF) have a series connection. Calculate the effective capacitance of this circuit.

Determine whether the two capacitors formed by four conducting plates each having an area "A" are connected in series or parallel.

Given two capacitors, their combined capacitance is 35 μF when connected in parallel. However, when they are arranged in series, the total capacitance decreases to 6.4 μF. What are the capacitance values for each capacitor individually?

Determine the ratio of the capacitances of the two capacitors, which, when connected in parallel store 8 times more energy than when connected in series to the same battery.

Two capacitors, 3.00 μF at 480 V and 4.50 μF at 520 V, are disconnected from their power sources. The positive plate of one is connected to the negative plate of the other. Determine the final potential difference and charge on each capacitor after connection.

As an engineer analyzing a multilayer ceramic capacitor with a maximum voltage rating of 200 V and a capacitance of 2.0 μF, you need to estimate the dielectric constant of the ceramic material. The capacitor has sheet dimensions of 10.0 mm by 15.0 mm, a total thickness of 8.0 mm (excluding the outer insulator), and a dielectric strength of 40 × 10⁶ V/m.

What are the potential differences and the charges on two capacitors of 1.0-μF and 2.0-μF, if they are connected to a 12.0-V battery in (i) series and (ii) in parallel?