Worked Examples-Calculation Part 1 - Static Electricity

Considered Formula;

$$\text {i)}\quad C = C_1 + C_2 \qquad \quad \Rightarrow \text {For parallel connection}$$ $$\qquad \text {Where}~~C \to Total~(Equivalent)~Capacitance,\\\qquad C_1 \to Capacitace~1 \\\qquad C_2 \to Capacitace~2$$

$$\text {ii)}\quad C = \frac {C_1 \times C_2}{C_1 + C_2} \qquad \quad \Rightarrow \text {For series connection}$$ $$\qquad \text {Where}~~C \to Total~(Equivalent)~Capacitance,\\\qquad C_1 \to Capacitace~1 \\\qquad C_2 \to Capacitace~2$$

Example 1

Two capacitors of 20 μF and 25 μF are connected in

a)    Series, and

b)    Parallel

What is the effective capacitance for (a) and (b)?

Solution

Data given

Capacitance 1 (C₁) = 20 μF

Capacitance 2 (C₂) = 25 μF

a)        In series connection

         Effective capacitance (C) = ?

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C = \frac {C_1 \times C_2}{C_1 + C_2}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {20 \times 25}{20 + 25}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {500}{45}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 11.11~\mu F$$

        The effective capacitance = 11.11 μF

b)        In parallel connection
         Effective capacitance (C) = ?

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C = C_1 + C_2$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 20 + 25$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 45~\mu F$$

      The effective capacitance = 45 μF